Question

Can someone please help me ASAP.....

Answer 1

We have to start with a number $x$, compute $f(x)$, and then use this result as input for $g(x)$

When you give $x$ as input to $f$, it returns $-x^2-1$:

$x\mapsto f(x)-x^2-1$

Now, $g(x)=x+5$ simply means that $g$ will return its input plus five.

In this case, the input is $f(x)$, so we have

$g(f(x))=f(x)+5 = -x^2-1+5=-x^2+4$