Find the inverse of fx7x4 Confirm by computing the function

Find the inverse of f(x)=7x-4. Confirm by computing the function composition (f • f^-1)(x) and (f^-1 • f)(x)

Solution

f(x) = 7x-4

Let y = 7x - 4

7x = y + 4

x = (y + 4)/7

So f^-1(x) = (x + 4)/7

Now (f • f^-1)(x) = f((x + 4)/7) = 7*((x + 4)/7) - 4 = x

and (f^-1 • f)(x) = f^-1(7x - 4) = (7x - 4 + 4)/7 = x