Question

assessment lep checkpoint
complete the following problems. show all your work.
learning goal from 10.1
i can determine the inverse of a function by solving f(x)=c. i can determine by composition that one function is the inverse of another, f(g(x))=x. i can determine the values of the inverse function from a graph or a table. i can describe the domain that will produce an invertible function from a non - invertible function.
what is the inverse of the following functions (1 point each)

1. f(x)=x^3 - 5

□ a. f^(-1)(x)=\sqrt3{x}-5
□ b. f^(-1)(x)=\sqrt3{x + 5}
□ c. f^(-1)(x)=\sqrt3{x}+5
□ d. the inverse does not exist

1. g(x)=2x^2 + 7

□ a. f^(-1)(x)=\frac{\sqrt{2x + 7}}{2}
□ b. f^(-1)(x)=(\frac{x - 7}{2})^(-1)
□ c. f^(-1)(x)=\sqrt{\frac{x - 7}{2}}
□ d. the inverse does not exist
lesson reflection (circle one)
starting... getting there... go

Explanation:

Step1: Let $y = f(x)$

Let $y=x^{3}-5$.

Step2: Solve for $x$ in terms of $y$

Add 5 to both sides: $y + 5=x^{3}$. Then take the cube - root of both sides: $x=\sqrt[3]{y + 5}$.

Step3: Replace $x$ with $f^{-1}(x)$ and $y$ with $x$

The inverse function $f^{-1}(x)=\sqrt[3]{x + 5}$.

For the function $g(x)=2x^{2}+7$, it is a non - one - to - one function (a parabola opening upwards), so its inverse does not exist without restricting the domain.

Answer:

1. B. $f^{-1}(x)=\sqrt[3]{x + 5}$
2. D. The inverse does not exist