Answer:
[tex]y\text{ =- }\sqrt[]{\frac{x+4}{3}\text{ }}\text{ -2 , x }\ge\text{-4}[/tex]
Explanation:
We start by getting the inverse of the function
Let g(x) = y
We go ahead to make x the subject of the formula as follows:
[tex]\begin{gathered} y=3(x+2)^2\text{ - 4} \\ y+4=3(x+2)^2 \\ \frac{y+4}{3}=(x+2)^2 \\ \\ x\text{ + 2 = }\sqrt[]{\frac{y+4}{3}} \\ \\ x\text{ = }\sqrt[]{\frac{y+4}{3}\text{ }}\text{ -2} \\ \\ \text{ We have finally:} \\ y\text{ = }\sqrt[]{\frac{x+4}{3}\text{ }}\text{ - 2} \end{gathered}[/tex]
Now,let us look at the restricton
The restriction are values that are less tahan or equal to -2
Values less than -2 are negative,so we pick the neagtive values and thus we have:
[tex]y\text{ =- }\sqrt[]{\frac{x+4}{3}\text{ }}\text{ -2 , x }\ge\text{-4}[/tex]
We are having a new restriction because x is inside a square root
