Question

Find the inverse of g(x) = -2x/3 -5

Answer 1

The condition for an inverse function is:

$g(x)=y\longrightarrow g^{-1}(y)=x$

Then, we can calculate:

$\begin{gathered} g(g^{-1}(x))=x \\ \frac{-2g^{-1}}{3}-5=x \\ -\frac{2}{3}\cdot g^{-1}=x+5 \\ g^{-1}=-\frac{3}{2}(x+5) \\ g^{-1}=-\frac{3}{2}x-\frac{15}{2} \end{gathered}$

The inverse of g(x) is:

$g^{-1}(y)=-\frac{3}{2}y-\frac{15}{2}$