F(x)=4x-4/5

Question

Find the inverse

Answer 1

First set f(x) = y

y = 4x - 4/5

Now swap x and y

x = 4y - 4/5

Solve for y

x + 4/5 = 4y - 4/5 + 4/5

x + 4/5 = 4y

(x + 4/5) / 4 = 4y / 4

x/4 + (4/5 x 1/4) = y

x/4 + 1/5 = y

Turn around

y = x/4 + 1/5

Now write with the inverse function notation:

f'(x) = x/4 + 1/5