What is the inverse of g(x)=(x+8)/3?

1 Answer
Jan 14, 2017

g^-1(x) = 3x - 8

Explanation:

Let y = g(x). So,

y = (x+8)/3

3y = x + 8

x = 3y - 8

g^-1(y) = 3y - 8.

Therefore,

g^-1(x) = 3x - 8


If we wanted, we could first prove that g is invertible, by showing that for any x_1,x_2inA, where A is the domain of g, g(x_1)=g(x_2)

x_1 = x_2, so x_1 + 8 = x_2 + 8 and (x_1 + 8)/3 = (x_2 + 8)/3

It holds that if x_1 = x_2, g(x_1) = g(x_2).

Thus, g is invertible.