Find the inverse of $$f\left(x\right)=-3\left(x+2\right)^3-1$$

$$f^{-1}\left(x\right)=\sqrt[3]{\frac{x+1}{-3}}-2$$

What is the inverse of $$f(x) = -(3x+1)^2-3$$ ?

$$f^{-1}(x)=\frac{\sqrt{-\left(x+3\right)}-1}{3}$$

Find the domain and range of the function.

Domain: [1, ∞) Range: (-∞, 4]

Why must we restrict the domain of a quadratic to make its inverse a function?

Because a quadratic is a many-to-one function.

What restrictions should be applied for the function to have an inverse that is a function? $$f\left(x\right)=2\left(x-1\right)^3+6$$

There are no restrictions needed since it is a cubic function (and its inverse, the cube root, is already a function).

What is the correct equation for the cube root graph pictured below, using the form $$f\left(x\right)=a\sqrt[3]{x-h}+k$$ ?

$$f\left(x\right)=-2\sqrt[3]{x+1}$$

Inverse functions and square roots

Flashcard

•

Mathematics

•

10th - 11th Grade

•

Practice Problem

•

Easy

•

TEKS

MATH.2A.2A, MATH.P.2E, MATH.2A.6K

Standards-aligned

Carrie Cummings

Used 6+ times

FREE Resource

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14 questions

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FLASHCARD QUESTION

Front

Back

Tags

TEKS.MATH.2A.2A

TEKS.MATH.2A.4C

FLASHCARD QUESTION

Front

Back

Tags

TEKS.MATH.P.2E

FLASHCARD QUESTION

Front

Was the inverse function found correctly?

Back

Tags

TEKS.MATH.P.2E

FLASHCARD QUESTION

Front

Back

Tags

TEKS.MATH.P.2E

FLASHCARD QUESTION

Front

Transformations of the function compared to the parent function?

Back

Reflected over the x-axis, vertical stretch by 2, and shifted right 5

Tags

TEKS.MATH.P.2G

FLASHCARD QUESTION

Front

Back

Tags

TEKS.MATH.2A.2A

TEKS.MATH.2A.4C

FLASHCARD QUESTION

Front

Identify the Range: (- ∞, -2 ], [ -2, ∞ ), All Real Numbers, [ 0, ∞)

Back

(- ∞, -2 ]

Tags

TEKS.MATH.2A.6K

TEKS.MATH.2A.7I

TEKS.MATH.A.2A

TEKS.MATH.A.6A

TEKS.MATH.A.9A

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