Question

F(x) = x2 + 2, g(x) = x2 - 1, h(x) = 3x Evaluate. g(h( f((-1))) =

Answer 1

The value of the composite function is $g(h(f(-1)))=80$

Step-by-step explanation:

In this problem we have the following functions:

$f(x)=x^2+2\\g(x)=x^2-1\\h(x)=3x$

We want to find the composite function

$g(h(f(x))$ and compute its value in x = -1.

In order to do that, we start by calculating the value of f(x) for x = -1:

$f(-1)=(-1)^2+2=1+2=3$

Now we compute $h(f(x))$ for x = -1:

$h(f(-1))=3(f(-1))=3(3)=9$

And now we compute $g(h(f(x)))$ for x = -1:

$g(h(f(-1)))= (h(f(-1))^2-1=9^2-1=80$

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