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gizmo_the_mogwai [7]
4 years ago
13

Given the definitions of f(x) and g(x) below, find the value of g(f(-3)).

Mathematics
1 answer:
ivanzaharov [21]4 years ago
8 0

Answer:

-11

Step-by-step explanation:

f(x) = 5x + 11

g(x) = x^2 + 4x - 11

g(f(-3)) = ?

f(-3) = 5(-3) + 11

= -15 + 11 = -4

g(f(-3)) = g(-4) = -(4)^2 + 4(-4) - 11

= 16 - 16 - 11 = -11

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<img src="https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B5%7D%7B8%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7B4%7D%20" id="TexFormula1" title
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-\dfrac{5}{8}+\dfrac{1}{4}=\dfrac{1}{4}+\left(-\dfrac{5}{8}\right)=\dfrac{1}{4}-\dfrac{5}{8}\\\\\text{find LCD:}\\\\8=2\cdot4,\ \text{therefore. LCD(4, 8) = 8}\\\\\dfrac{1}{4}=\dfrac{1\cdot2}{4\cdot2}=\dfrac{2}{8}\\\\\text{continuing}\\\\=\dfrac{2}{8}-\dfrac{5}{8}=\dfrac{2-5}{8}=-\dfrac{3}{8}

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