Answer:
[tex]g^{-1}(x) = -\frac{x}{3} -6[/tex]
Step-by-step explanation:
suppose g⁻¹(x) = y
g⁻¹(x) = y ⇔ g(y) = x
Here we have to work out y ,in order to determine
the inverse function g⁻¹.
g(y) = x
⇔ -3(y + 6) = x
[tex]\Longleftrightarrow (y+6) =- \frac{x}{3}[/tex]
[tex]\Longleftrightarrow y =- \frac{x}{3} -6[/tex]
Therefore,
[tex]g^{-1}(x) = -\frac{x}{3} -6[/tex]
