If $$f\left(x\right)=4-\sqrt{3x-6}$$ and $$g\left(x\right)=x+2$$ find $$f\circ\ g\left(x\right)$$ and $$f\ \circ\ g\left(5\right).$$

$$f\circ\ g\left(x\right)=4\ -\sqrt{3x}$$ and $$f\ \circ\ g\left(5\right)\ \approx.127$$

$$f\circ\ g\left(x\right)=4\ -\sqrt{3x+12}$$ and $$f\ \circ\ g\left(5\right)\ \approx.127$$

$$f\circ\ g\left(x\right)=4\ -\sqrt{3x+12}$$ and $$f\ \circ\ g\left(5\right)\ \approx8.24$$

$$f\circ\ g\left(x\right)=4\ -\sqrt{3x}$$ and $$f\ \circ\ g\left(5\right)\ \approx4.67$$

Given $$j\left(x\right)=\sqrt[3]{x-10}$$ and $$k\left(x\right)=x^3,$$ find $$j\ \circ\ k$$ and $$j\left(k\left(1\right)\right).$$

$$j\ \circ\ k\ =\ \sqrt[3]{x^3-10}$$ and $$j\left(k\left(1\right)\right)=-3.$$

$$j\ \circ\ k\ =\ \sqrt[3]{x^3-10}$$ and $$j\left(k\left(1\right)\right)=-9.$$

$$j\ \circ\ k\ =\ x-10$$ and $$j\left(k\left(1\right)\right)=-9.$$

$$j\ \circ\ k\ =\ x-10$$ and $$j\left(k\left(1\right)\right)=-3.$$

Given $$j\left(x\right)=\sqrt[3]{x-10}$$ and $$k\left(x\right)=x^3,$$ find $$k\ \circ\ j$$ and $$k\left(j\left(1\right)\right).$$

$$k\ \circ\ j=\ x-10$$ and $$k\left(j\left(1\right)\right)=-9.$$

$$k\ \circ\ j=\ x-10$$ and $$k\left(j\left(1\right)\right)=-3.$$

$$k\ \circ\ j=\ \sqrt[3]{x^3-10}$$ and $$k\left(j\left(1\right)\right)=-3.$$

$$k\ \circ\ j=\ x^3-10$$ and $$k\left(j\left(1\right)\right)=-9.$$

Let $$z\left(t\right)=\sqrt{t+8.}$$ Find $$z^{-1}.$$ What is the domain of $$z^{-1}$$ ?

$$f^{-1}\left(x\right)=\ x^2-8$$ domain: $$x\ \ge\ 0$$

$$f^{-1}\left(x\right)=\ x^2-8$$ domain: $$x\ \ge\ -8$$

$$f^{-1}\left(x\right)=\ \left(x-8\right)^2$$ domain: $$x\ \ge\ 0$$

$$f^{-1}\left(x\right)=\ \left(x-8\right)^2$$ domain: $$x\ \ge\ -8$$

The function p(x) = 5(x − 3)² is not one-to-one. Restrict its domain so that the resulting function is one-to-one. Then, find the inverse of the function with the restricted domain.

$$f^{-1}\left(x\right)=\sqrt{\frac{x}{5}}+3$$ domain: $$x\ \ge\ 3$$

$$f^{-1}\left(x\right)=\sqrt{\frac{x}{5}+3}$$ domain: $$x\ \ge\ 0$$

$$f^{-1}\left(x\right)=\sqrt{\frac{x}{5}}+3$$ domain: $$x\ \ge\ 0$$

$$f^{-1}\left(x\right)=\sqrt{\frac{x}{5}+3}$$ domain: $$x\ \ge\ 3$$

Unit 1 Review: Functions

Authored by Megan Weber

Mathematics

10th Grade

CCSS covered

Used 2+ times

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

Given the table of a one-to-one function, find ƒ¯¹(6) and ƒ(ƒ¯¹(9)).

Tags

CCSS.HSF-BF.B.4C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The graph of function ƒ is given. Find ƒ(4) and ƒ(ƒ(1)).

Tags

CCSS.HSF.IF.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

-7

-9

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CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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CCSS.HSF-BF.B.4A

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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CCSS.HSF-BF.A.1C

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

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CCSS.HSF-BF.A.1C

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