Question

3. Se f(x) = 2x + 1 e f(9(x)) = X2 - 1, determine a função g(x).

Answer 1

Resposta:

Dados:

$f(x) = 2x + 1;\\\\f(g(x)) = x^{2} - 1.$

Temos:

$f(g(x)) = 2[g(x)] + 1\\\\2[g(x)] + 1 = x^{2} - 1\\\\2[g(x)] = x^{2} - 2\\\\g(x) = \frac{1}{2}x^{2} - 1$