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

Jan 14, 2017

${g}^{-} 1 \left(x\right) = 3 x - 8$

#### Explanation:

Let $y = g \left(x\right)$. So,

$y = \frac{x + 8}{3}$

$3 y = x + 8$

$x = 3 y - 8$

${g}^{-} 1 \left(y\right) = 3 y - 8$.

Therefore,

${g}^{-} 1 \left(x\right) = 3 x - 8$

If we wanted, we could first prove that $g$ is invertible, by showing that for any ${x}_{1} , {x}_{2} \in A$, where $A$ is the domain of $g$, $g \left({x}_{1}\right) = g \left({x}_{2}\right)$

${x}_{1} = {x}_{2}$, so ${x}_{1} + 8 = {x}_{2} + 8$ and $\frac{{x}_{1} + 8}{3} = \frac{{x}_{2} + 8}{3}$

It holds that if ${x}_{1} = {x}_{2}$, $g \left({x}_{1}\right) = g \left({x}_{2}\right)$.

Thus, $g$ is invertible.