Find the inverse function

Question

Find the inverse function of f.

f(x) = x

x + 8

f ⁻¹(x) = 

 

Answer 1

Assuming that this is y = x/(x+8), you solve for inverses by solving for x in terms of y.

y = x/(x+8)

Multiplying both sides by x+8,

y(x+8) = x

xy + 8y = x

8y = x - xy

8y = x(1-y)

8y/(1-y) = x

Substituting x for y,

f^-1(x) = 8x/(1-x)

Answer 2

f(x) = x / (x+8)

y = x/(x+8)

Solve for x: y(x+8) = x

xy - x = -8y

x(y - 1) = -8y

x = -8y / (y - 1)

Switch x and y to get y = -8x / (x - 1)

So, f^-1(x) = -8x / (x - 1)