Question

Dadas as funções f(x) = 4x² - 5 e g(x) = 2x + 2, determinar as compostas de f(g(x)) e g(f(x)).

Answer 1

Resposta:

Encontremos a função composta f(g(x)):

$f[g(x)] = 4[g(x)]^{2} - 5\\\\= 4(2x + 2)^{2} - 5\\\\= 4(4x^{2}+8x + 4) - 5\\\\= 16x^{2} + 32x + 16 - 5\\\\= 16x^{2} + 32x + 11.$

Encontremos a função composta g(f(x)):

$g[f(x)] = 2[f(x)] + 2\\\\= 2(4x^{2} - 5) + 2\\\\= 8x^{2} - 10 + 2\\\\= 8x^{2} - 8.$