Question

For the function f(x)=5x-2, find f^-1(x)

Answer 1

Answer:

$f^{-1}(x)=\frac{x+2}{5}$

Explanation:

Given the below function;

$f(x)=5x-2$

We can go ahead and find the inverse of f(x) following the below steps;

Step 1: Replace f(x) with y;

$y=5x-2$

Step 2: Interchange x and y;

$x=5y-2$

Step 3: Solve for y by adding 2 to both sides of the equation and dividing both sides by 5;

$\begin{gathered} x+2=5y-2+2 \\ x+2=5y \\ \frac{x+2}{5}=y \\ y=\frac{x+2}{5} \end{gathered}$

Step 4: Replace y with f^-1(x);

$f^{-1}(x)=\frac{x+2}{5}$