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

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Mathematics

•

10th - 11th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF-IF.C.7B, HSF-BF.B.4A, HSF-BF.B.4D

Standards-aligned

Carrie Cummings

Used 6+ times

FREE Resource

Student preview

14 questions

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FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7B

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Was the inverse function found correctly?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

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

CCSS.HSF.BF.B.3

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-IF.C.7B

FLASHCARD QUESTION

Front

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

Back

(- ∞, -2 ]

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