Question

If f(x) = (x - 3)/(x + 4), find f -1(x).

Answer 1

f^-1(x) = (4x +3)/(1 -x)

Explanation:

Solve for y:

f(y) = x

(y -3)/(y +4) = x

y -3 = xy +4x . . . . . . multiply by y+4

y -xy = 4x +3 . . . . . . add 3-xy

y(1 -x) = 4x +3 . . . . . factor out y

y = (4x +3)/(1 -x) . . . divide by the coefficient of y

The inverse function is ...

f^-1(x) = (4x +3)/(1 -x)