Find the inverse function of f

Question

Find the inverse function of f.

f(x) = 4x + 7

f ⁻¹(x) = 

 

Answer 1

First, you want to express f(x) as y so that you can write your equation as y = 4x+7. Now you can swap the x and y, giving x = 4y+7. Solving for y, you find y = (x-7)/4, which is in your inverse function f^-1(x).

To confirm that this is correct, you can plug this into your original function, and the result should be f(f^-1(x)) = x.

In this case, f(f^-1(x)) = 4((x-7)/4 + 7) = x - 7 + 7 = x.