Answer:
[tex]f(g(-4)) = 18[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 4x + 6[/tex]
[tex]g(x) = x^2 + x - 9[/tex]
Required
Find f(g(-4))
First, calculate f(g(x))
We have:
[tex]f(x) = 4x + 6[/tex]
[tex]f(g(x)) = 4g(x) + 6[/tex]
Substitute: [tex]g(x) = x^2 + x - 9[/tex]
[tex]f(g(x)) = 4[x^2 + x - 9] + 6[/tex]
Open bracket
[tex]f(g(x)) = 4x^2 + 4x - 36 + 6[/tex]
[tex]f(g(x)) = 4x^2 + 4x-30[/tex]
Substitute [tex]-4[/tex] for [tex]x[/tex]
[tex]f(g(-4)) = 4*(-4)^2 + 4*(-4)-30[/tex]
[tex]f(g(-4)) = 64 -16 -30[/tex]
[tex]f(g(-4)) = 18[/tex]
