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Given the definitions of f(x) and g(x)
below, find the value of f(g(-4)). F(x)=4x+6 g(x)=x^ 2+x-9

Sagot :

MrRoyalidn

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]

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