Complete the statement: f − 1 ( f ( y ) ) = y f o r e v e r y y i n t h e . . . f^{-1}\left(f\left(y\right)\right)=y\ \ for\ every\ y\ in\ the... f − 1 ( f ( y ) ) = y f o r e v e r y y i n t h e . . .

domain of f − 1 f^{-1} f − 1

Find the exact value of cos ⁡ − 1 ( 3 2 ) \cos^{-1}\left(\frac{\sqrt{3}}{2}\right) cos − 1 ( 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> )

− π 3 -\frac{\pi}{3} − 3 π

− π 6 -\frac{\pi}{6} − 6 π

Find the exact value of sec ⁡ − 1 ( − 2 ) \sec^{-1}\left(-2\right) sec − 1 ( − 2 )

− π 3 -\frac{\pi}{3} − 3 π

− 2 π 3 -\frac{2\pi}{3} − 3 2 π

Find the exact value of csc ⁡ − 1 ( 2 3 3 ) \csc^{-1}\left(\frac{2\sqrt{3}}{3}\right) csc − 1 ( 3 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> )

− π 3 -\frac{\pi}{3} − 3 π

Find the exact value of tan ⁡ − 1 ( − 1 ) \tan^{-1}\left(-1\right) tan − 1 ( − 1 )

− π 4 -\frac{\pi}{4} − 4 π

Find the exact value of tan ⁡ ( cot ⁡ − 1 ( 3 ) ) \tan\left(\cot^{-1}\left(\sqrt{3}\right)\right) tan ( cot − 1 ( 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> ) )

3 3 \frac{\sqrt{3}}{3} 3 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

3 \sqrt{3} 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

Find the exact value of sec ⁡ ( tan ⁡ − 1 ( 3 3 ) ) \sec\left(\tan^{-1}\left(\frac{\sqrt{3}}{3}\right)\right) sec ( tan − 1 ( 3 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> ) )

2 3 3 \frac{2\sqrt{3}}{3} 3 2 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

2 \sqrt{2} 2 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

For this question, you are allowed to use a scratch paper. Solve the equation: 4 tan ⁡ − 1 ( x ) = − π 4\tan^{-1}\left(x\right)=-\pi 4 tan − 1 ( x ) = − π

3 \sqrt{3} 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

3 3 \frac{\sqrt{3}}{3} 3 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" />

Find the exact value of cos ⁡ − 1 ( − 1 2 ) \cos^{-1}\left(-\frac{1}{2}\right) cos − 1 ( − 2 1 )

− π 3 -\frac{\pi}{3} − 3 π

Find the exact value of cot ⁡ − 1 ( − 3 3 ) \cot^{-1}\left(-\frac{\sqrt{3}}{3}\right) cot − 1 ( − 3 3 <path d="M 95 702 c -2.7 0 -7.17 -2.7 -13.5 -8 c -5.8 -5.3 -9.5 -10 -9.5 -14 c 0 -2 0.3 -3.3 1 -4 c 1.3 -2.7 23.83 -20.7 67.5 -54 c 44.2 -33.3 65.8 -50.3 66.5 -51 c 1.3 -1.3 3 -2 5 -2 c 4.7 0 8.7 3.3 12 10 s 173 378 173 378 c 0.7 0 35.3 -71 104 -213 c 68.7 -142 137.5 -285 206.5 -429 c 69 -144 104.5 -217.7 106.5 -221 c 5.3 -9.3 12 -14 20 -14 H 400000 v 40 H 845.272 s -225.272 467 -225.272 467 s -235 486 -235 486 c -2.7 4.7 -9 7 -19 7 c -6 0 -10 -1 -12 -3 s -194 -422 -194 -422 s -65 47 -65 47 Z M 834 80 H 400000 v 40 H 845 Z" /> )

− π 3 -\frac{\pi}{3} − 3 π

Inverse Trigonometric Functions

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Practice Problem

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Hard

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CCSS

HSF.TF.B.7, HSF-BF.B.4D, HSF.BF.B.4

Standards-aligned

Carlos Doctolero

Used 75+ times

FREE Resource

15 questions

Show all answers

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

What test will you use to determine if a function is one-to-one?

Veetical Line Test

Horizontal Line Test

One-to-one Test

Function Domain-Range Test

Tags

CCSS.HSF.BF.B.4

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Complete the statement:

$f^{-1}\left(f\left(y\right)\right)=y\ \ for\ every\ y\ in\ the...$

domain of $f$

range of $f$

set of real numbers

domain of $f^{-1}$

Tags

CCSS.HSF-BF.B.4B

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

$-\frac{\pi}{3}$

$\frac{\pi}{3}$

$-\frac{\pi}{6}$

$\frac{\pi}{6}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

What is the domain of the inverse cotangent function?

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

$\left[0,\pi\right]$

$\left(-\infty,+\infty\right)$

$\left(-1,1\right)$

Tags

CCSS.HSF-BF.B.4D

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\sec^{-1}\left(-2\right)$

$\frac{2\pi}{3}$

$-\frac{\pi}{3}$

$\frac{4\pi}{3}$

$-\frac{2\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\tan\left(\tan^{-1}\left(\theta\right)\right)\ if\ \theta=2$

Undefined

Can't be determined

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\sec^{-1}\left(\sec\left(\frac{\pi}{2}\right)\right)$

$\frac{\pi}{2}$

Undefined

Can't be determined

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\csc^{-1}\left(\frac{2\sqrt{3}}{3}\right)$

$\frac{2\pi}{3}$

$-\frac{\pi}{3}$

$\frac{\pi}{6}$

$\frac{\pi}{3}$

Tags

CCSS.HSF.TF.B.7

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

Find the exact value of $\tan^{-1}\left(-1\right)$

$\frac{\pi}{4}$

$\frac{3\pi}{4}$

$-\frac{\pi}{4}$

$\frac{7\pi}{4}$

Tags

CCSS.HSF.TF.B.7

10.

MULTIPLE CHOICE QUESTION

20 sec • 1 pt

What is the restricted domain of the cosine function in order to have an inverse cosine function?

$\left[0,\pi\right]\ -\ \left\{\frac{\pi}{2}\right\}$

$\left[0,\pi\right]$

$\left[-1,1\right]$

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

Tags

CCSS.HSF-BF.B.4D

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Inverse Trigonometric Functions

15 questions

What test will you use to determine if a function is one-to-one?

Complete the statement: f−1(f(y))=y for every y in the...f^{-1}\left(f\left(y\right)\right)=y\ \ for\ every\ y\ in\ the...f−1(f(y))=y for every y in the...

Find the exact value of cos⁡−1(32)\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)cos−1(23​​)

What is the domain of the inverse cotangent function?

Find the exact value of sec⁡−1(−2)\sec^{-1}\left(-2\right)sec−1(−2)

Find the exact value of tan⁡(tan⁡−1(θ)) if θ=2\tan\left(\tan^{-1}\left(\theta\right)\right)\ if\ \theta=2tan(tan−1(θ)) if θ=2

Find the exact value of sec⁡−1(sec⁡(π2))\sec^{-1}\left(\sec\left(\frac{\pi}{2}\right)\right)sec−1(sec(2π​))

Find the exact value of csc⁡−1(233)\csc^{-1}\left(\frac{2\sqrt{3}}{3}\right)csc−1(323​​)

Find the exact value of tan⁡−1(−1)\tan^{-1}\left(-1\right)tan−1(−1)

What is the restricted domain of the cosine function in order to have an inverse cosine function?

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Complete the statement:

$f^{-1}\left(f\left(y\right)\right)=y\ \ for\ every\ y\ in\ the...$

Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

Find the exact value of $\sec^{-1}\left(-2\right)$

Find the exact value of $\tan\left(\tan^{-1}\left(\theta\right)\right)\ if\ \theta=2$

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Find the exact value of $\csc^{-1}\left(\frac{2\sqrt{3}}{3}\right)$

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