Question

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

Answer 1

`f^(-1)(x)=(x+2)/(5)`

Step-by-step 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 \\ (x+2)/(5)=y \\ y=(x+2)/(5) \end{gathered}`

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

`f^(-1)(x)=(x+2)/(5)`