If $f(x)=x^4$ and $g(x)=3(x+2)$, find the value of each expression below.

1. $f(2)$ 

   Answer (a):

   $16$

2. $g(2)$ 

3. $f(g(2))$ 

   Hint (c):

   Substitute the output for $g(2)$ into $f(x)$.

   Answer (c):

   $20,736$

4. $g(f(2))$ 

5. Are $f(x)$ and $g(x)$ inverses of each other? Justify your answer.

   Hint (e):

   What happens to the original input when the two functions are inverses?