If $f(x) = x^2 + 5$ and $g(x) = x + 3$, write and simplify expressions for the function operations given below.

1. $f(g(x))$

   Hint (a):

   $f(g(x)) = f(x + 3) =$ ______________

2. $g(f(x))$

   Hint (b):

   Refer to hint (a).

3. $f^{ −1}(−6)$

   Hint (c):

   Even though $f^{ −1}(x)$ is the inverse of $f(x)$, you do not need to find the equation of the inverse. Simply evaluate $6$ as the $y$-value and solve for $x$.

   Answer (c):

   $6 = f(x)$
   $6 = x^2 + 5$
   $1 = x^2$
   $x = ± 1$

4. $g^{−1}(−6)$

   Hint (d):

   Refer to hint (c).