Sure, let's solve this step-by-step.
We are given two functions:
[tex]\[ h(x) = x^2 - 3 \][/tex]
[tex]\[ k(x) = 5 + x \][/tex]
We are asked to find [tex]\( k(h(0)) \)[/tex].
1. Calculate [tex]\( h(0) \)[/tex]:
[tex]\[
h(0) = 0^2 - 3 = -3
\][/tex]
2. Calculate [tex]\( k(h(0)) \)[/tex]:
First, substitute the result from [tex]\( h(0) \)[/tex] into [tex]\( k(x) \)[/tex]:
[tex]\[
k(h(0)) = k(-3)
\][/tex]
Now, compute [tex]\( k(-3) \)[/tex]:
[tex]\[
k(-3) = 5 + (-3) = 2
\][/tex]
So, the value of [tex]\( k(h(0)) \)[/tex] is [tex]\(\boxed{2}\)[/tex].
Out of the given choices:
[tex]\[ 2, 5, -3, 0 \][/tex]
The correct answer is:
[tex]\[ 2 \][/tex]
