The inverse function is:
[tex]g(x) = 27*x^3 - 4[/tex]
And g(2) = 212.
How to get the inverse function?
We need to find g(x) such that:
g(h(x)) = x.
We know that:
[tex]h(x) = \frac{\sqrt[3]{x + 4} }{3}[/tex]
Then our function must be a cubic, multiplied by 3^3 = 27, and then subtracts 4, it is:
[tex]g(x) = 27*x^3 - 4[/tex]
As you can see, if you evaluate in h(x), the outcome is x.
Now we can evaluate this in x = 2, we get:
[tex]g(2) = 27*2^3 - 4 = 212[/tex]
The correct option is C.
If you want to learn more about inverses.
https://brainly.com/question/14391067
#SPJ1
