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 \\ (-2g^(-1))/(3)-5=x \\ -(2)/(3)\cdot g^(-1)=x+5 \\ g^(-1)=-(3)/(2)(x+5) \\ g^(-1)=-(3)/(2)x-(15)/(2) \end{gathered}`

The inverse of g(x) is:

`g^(-1)(y)=-(3)/(2)y-(15)/(2)`