Question

Let f(x)=7x-13. Find f^-1(x).

Answer 1

Ok but allow my humble self to use
`y` instead of
`f(x)`.

We have,

`y=7x-13`

If you wanna know what the inverse is swap the values of x and y,

`x=7y-13`

And now solve for y,

`x+13=7y\implies\boxed{y=f^(-1)(x)=(x+13)/(7)}`.

Hope this helps.

Answer 2

The inverse function is (x+13)/7

Explanation:

y = 7x-13

Exchange x and y

x = 7y -13

Solve for y

Add 13 to each side

x+13 = 7y-13+13

x+13 = 7y

Divide each side by 7

(x+13)/7 = 7y/7

(x+13)/7 = y

The inverse function is (x+13)/7