Question

Dadas as funções reais f(x)=$x^{2}$ e g(x)=x+2; calcule fog f(-2)

Answer 1

Achando fog:

$f(x)=x^{2}\\f(g(x))=[g(x)]^{2}\\fog(x)=(x+2)^{2}\\fog(x)=x^{2}+2*x*2+2^{2}\\fog(x)=x^{2}+4x+4$
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Calculando f(-2):

$f(x)=x^{2}\\f(-2)=(-2)^{2}\\f(-2)=4$
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$fog(f(-2))=fog(4)\\\\fog(x)=x^{2}+4x+4\\fog(4)=4^{2}+4*4+4\\fog(f(-2))=16+16+4\\fog(f(-2))=36$