Question

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

Answer 1

Answer:

The inverse function is (x+13)/7

Step-by-step 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

Answer 2

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,

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

Hope this helps.