Angelica is working with two function machines, $g ( x ) = \sqrt { x - 5 }$ and  $h(x)=x^2-6$. She wants to stack the two machines so that the output of the first machine becomes the input of the second. Her beginning input is $6$.

1. In what order must she put the machines to get a final output of $5$?

   Hint 1 (a):

   Try substituting $6$ for $x$ in $g(x)$ and then input the result into $h(x)$. If that does not work, switch the order.

   Step 1 (a):

   Substitute $6$ for each $x$.

   Step 2 (a):

   Simplify.

   Step 3 (a):

   Substitute the output of the first function for $x$ in the second function.

   $g(x)=\sqrt{x-5}$

   $g(6)=1$

   $h(1)=1^{2}-6$

2. Is it possible for her to get a final output of $-5$? If so, show how she could do that. If not, explain why not.

   Answer (b):

   See above (original incorrect solution).