Question

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Sendo F(x)=3x-10, G(x)=2x+2 e H(x)=2x+2 Calcule:

16/3

20/3

28/3

32/3

35/3

Answer 1

Explicação passo-a-passo:

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Temos as seguinte funções:

$\boxed{f(x)=3x-10}$

$\boxed{g(x)=2x+2}$

$\boxed{h(x)=2x+2}$

Calculando a função inversa de f:

$f(x)=3x-10\\\\y=3x-10\\\\\text{Trocando x por y e y por x:}\\\\x=3y-10\\\\3y=x+10\\\\y=\dfrac{x+10}{3}\\\\\boxed{f^{-1} (x) =\dfrac{x+10}{3}}$

Calculando h(3):

$h(3)=2.3+2\\\\h(3)=6+2\\\\\boxed{h(3)=8}$

Calculando g(h(3)):

$g(h(3))=g(8)\\\\g(h(3))=2.8+2\\\\g(h(3))=16+2\\\\\boxed{g(h(3))=18}$

Calculando $f^{-1}(g(h(3)))$ :

$f^{-1}(g(h(3))) =f^{-1}(18) \\\\f^{-1}(g(h(3))) =\dfrac{18+10}{3} \\\\\boxed{\boxed{f^{-1}(g(h(3))) =\dfrac{28}{3}}}$