f(x) = 6/5x - 3 find the inverse

Answer 1

The inverse of a function is the reflection across the line y=x. So to find the inverse, we switch x and y and solve for y.

f(x) = (6/5)x - 3

1. Replace f(x) with y: y= (6/5)x - 3
2. Switch x and y: x= (6/5)y - 3
3. Solve for y: x + 3 = (6/5)y (5/6)(x+3) = y

y = (5/6)x + (5/2)

f^-1(x) = (5/6)x + (5/2)

Answer 2

Change f(x) to y, switch x and y, then solve for y. Your new y becomes f^-1(x).

x = (6/5)y - 3

x + 3 = (6/5)y

(5/6)(x + 3) = (5/6)(6/5)y

y = (5x + 15)/6

y = (5/6)x + 15/6

f^-1(x) = (5/6)x + 5/2