Question

talib is trying to find the inverse of the function to the right. his work appears beneath it. is his work correct? explain your answer.

f(x)= -8x + 4

y = -8x + 4

y - 4 = -8x

x=(y - 4)/-8

f^(-1)(x)=(y - 4)/-8

Explanation:

Step1: Start with the original function

Given $f(x)= - 8x + 4$, let $y = f(x)$, so $y=-8x + 4$.

Step2: Solve for x in terms of y

First, subtract 4 from both sides: $y - 4=-8x$. Then divide both sides by -8: $x=\frac{y - 4}{-8}$.

Step3: Find the inverse function

Replace x with $f^{-1}(y)$: $f^{-1}(y)=\frac{y - 4}{-8}$. Usually, we write the inverse function in terms of x, so $f^{-1}(x)=\frac{x - 4}{-8}$.

Answer:

Talib's work is correct. He correctly followed the steps of finding the inverse of a linear - function. First, he replaced $f(x)$ with y. Then he solved for x in terms of y by isolating x. Finally, he replaced x with $f^{-1}(x)$ to get the inverse function.