Angelica is working with function machines. She has the two machines $g\left(x\right)=\sqrt{x-5}$ and $h(x)=x^2−6$. She wants to put them in order so that the output of the first machine becomes the input of the second. She wants to use a beginning input of $6$.

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 $x$.

   $g(6)=\sqrt{6-5}$

   Step 2(a):

   Simplify.

   $g(6)=1$

   Step 3(a):

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

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

   Answer (a):

   The output needs to be $5$.

   

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).