Question

sendo f(x)=4+× e g(x)= x²+2. Determine o valor de f-¹ (g(x-2)). ​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo-a-passo:

$\sf f(x) = 4 + x$

$\sf x = 4 + y$

$\sf y = x - 4$

$\sf f^{-1}(x) = x - 4$

$\sf g(x) = x^2 + 2$

$\sf g(x- 2) = (x - 2)^2 + 2$

$\sf g(x- 2) = (x^2 - 4x + 4) + 2$

$\sf g(x- 2) = x^2 - 4x + 6$

$\sf f^{-1}(g(x-2)) = x^2 - 4x + 6 - 4$

$\boxed{\boxed{\sf f^{-1}(g(x-2)) = x^2 - 4x + 2}}$