Answer :

To solve the problem, we are given two functions: [tex]\( f(x) = x^2 - 2 \)[/tex] and [tex]\( h(x) = x^3 - 1 \)[/tex]. We need to find the value of [tex]\( f(h(-2)) \)[/tex].

Here's the step-by-step process:

1. Calculate [tex]\( h(-2) \)[/tex]:

- Start with the function [tex]\( h(x) = x^3 - 1 \)[/tex].
- Substitute [tex]\( x = -2 \)[/tex] into the function:
[tex]\[
h(-2) = (-2)^3 - 1
\][/tex]
- Calculate [tex]\( (-2)^3 = -8 \)[/tex], therefore:
[tex]\[
h(-2) = -8 - 1 = -9
\][/tex]

2. Calculate [tex]\( f(h(-2)) \)[/tex], which is [tex]\( f(-9) \)[/tex]:

- Use the function [tex]\( f(x) = x^2 - 2 \)[/tex].
- Substitute [tex]\( x = -9 \)[/tex] into the function:
[tex]\[
f(-9) = (-9)^2 - 2
\][/tex]
- Calculate [tex]\( (-9)^2 = 81 \)[/tex], therefore:
[tex]\[
f(-9) = 81 - 2 = 79
\][/tex]

So, the final answer is [tex]\( f(h(-2)) = 79 \)[/tex].

Thanks for taking the time to read If tex f x x 2 2 tex and tex h x x 3 1 tex then find tex f h 2 tex A 79. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada