Question

dada as funções f (x) = 2x elevado a 2 -6x-4 e g(x) = -3elevado a 2 - 5x+1 calcule ​

Answer 1

Resposta:

Explicação passo-a-passo:

f(x)=3x+4\\g(x)=2x-1

Calculando a inversa de g:

g(x)=2x-1\\x=2g^{-1}(x)-1\\x+1=2g^{-1}(x)\\(x+1)/2=g^{-1}(x)

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g^{-1}(x)=(x+1)/2\\g^{-1}(f(x))=(f(x)+1)/2\\g^{-1}(f(x))=(3x+4+1)/2\\g^{-1}(f(x))=(3x+5)/2

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Calculando f(g(2)):

g(x)=2x-1\\g(2)=2.2-1\\g(2)=4-1\\g(2)=3\\\\f(g(2))=f(3)\\f(g(2))=3.3+4\\f(g(2))=9+4\\f(g(2))=13

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Finalmente:

g^{-1}(f(x))=f(g(2))\\g^{-1}(f(x))=13\\(3x+5)/2=13\\3x+5=2.13\\3x+5=26\\3x=26-5\\3x=21\\x=21/3\\x=7