Answer:
[tex]h(g(-5)) = 127[/tex]
Explanation:
Given
[tex]h(x) = 2x^2 - 1[/tex]
[tex]g(x) = x - 3[/tex]
Required
Find [tex]h(g(-5))[/tex]
First, we need to solve for [tex]g(-5)[/tex]
[tex]g(x) = x - 3[/tex]
Substitute -5 for x
[tex]g(-5) = -5 - 3[/tex]
[tex]g(-5) = -8[/tex]
Substitute -8 for g(-5) in [tex]h(g(-5))[/tex]
[tex]h(g(-5))[/tex] = [tex]h(-8)[/tex]
Given that:
[tex]h(x) = 2x^2 - 1[/tex]
Substitute -8 for x
[tex]h(-8) = 2(-8)^2 - 1[/tex]
[tex]h(-8) = 2*64 - 1[/tex]
[tex]h(-8) = 128 - 1[/tex]
[tex]h(-8) = 127[/tex]
Hence:
[tex]h(g(-5)) = 127[/tex]
