Question

Keith used the following steps to find the inverse of f, but he thinks he made an error. Given f(x) = 7x + 5, what is the correct inverse of f?

1) g(x) = (x - 5)/7
2) g(x) = (x + 5)/7
3) g(x) = (x - 5)/7 + 5
4) g(x) = (x + 5)/7 - 5

Answer 1

To find the inverse of a function, replace f(x) with y, interchange x and y, solve for y, and replace y with the function notation g(x). The correct inverse of f(x) = 7x + 5 is g(x) = (x - 5)/7.

Step-by-step explanation:

To find the inverse of a function, we can follow a few steps:

1. Replace the function notation f(x) with y.
2. Interchange the x and y variables.
3. Solve the new equation for y.
4. Replace y with the function notation g(x).

Let's apply these steps to the given function f(x) = 7x + 5:

1. Replace f(x) with y: y = 7x + 5.
2. Interchange x and y: x = 7y + 5.
3. Solve for y: y = (x - 5)/7.
4. Replace y with g(x): g(x) = (x - 5)/7.

Therefore, the correct inverse of f is option 1) g(x) = (x - 5)/7.