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Answer :
We are given the functions
[tex]$$
f(x)=x^2-2 \quad \text{and} \quad h(x)=x^3-1.
$$[/tex]
Step 1: Evaluate [tex]$h(-2)$[/tex]
Substitute [tex]$x=-2$[/tex] into the function [tex]$h(x)$[/tex]:
[tex]$$
h(-2)=(-2)^3-1.
$$[/tex]
Since
[tex]$$
(-2)^3=-8,
$$[/tex]
we have
[tex]$$
h(-2)=-8-1=-9.
$$[/tex]
Step 2: Evaluate [tex]$f(h(-2))$[/tex]
Now substitute [tex]$h(-2) = -9$[/tex] into [tex]$f(x)$[/tex]:
[tex]$$
f(-9)=(-9)^2-2.
$$[/tex]
Since
[tex]$$
(-9)^2=81,
$$[/tex]
we find
[tex]$$
f(-9)=81-2=79.
$$[/tex]
Thus, the final answer is [tex]$\boxed{79}$[/tex].
[tex]$$
f(x)=x^2-2 \quad \text{and} \quad h(x)=x^3-1.
$$[/tex]
Step 1: Evaluate [tex]$h(-2)$[/tex]
Substitute [tex]$x=-2$[/tex] into the function [tex]$h(x)$[/tex]:
[tex]$$
h(-2)=(-2)^3-1.
$$[/tex]
Since
[tex]$$
(-2)^3=-8,
$$[/tex]
we have
[tex]$$
h(-2)=-8-1=-9.
$$[/tex]
Step 2: Evaluate [tex]$f(h(-2))$[/tex]
Now substitute [tex]$h(-2) = -9$[/tex] into [tex]$f(x)$[/tex]:
[tex]$$
f(-9)=(-9)^2-2.
$$[/tex]
Since
[tex]$$
(-9)^2=81,
$$[/tex]
we find
[tex]$$
f(-9)=81-2=79.
$$[/tex]
Thus, the final answer is [tex]$\boxed{79}$[/tex].
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