Question

Let f(x) = 4x + 7. Find f-1(15)

Answer 1

$f(x)=4x+7$

1. replace f(x) with y

$y=4x+7$

2. Replace every x with a y and replace every y with an x

$x=4y+7$

3. Solve for y:

$\begin{gathered} 4y=x-7 \\ y=\frac{x-7}{4} \end{gathered}$

4. Replace y with f−1(x):

$f^{-1}(x)=\frac{x-7}{4}$

Evaluate the inverse for x = 15:

$f^{-1}(15)=\frac{15-7}{4}=\frac{8}{4}=2$