Question

sendo f(x) = x² -1 e g(x) = x+2 então o conjunto solução da equação f(g(x)) =0 é?

Answer 1

Explicação passo-a-passo:

Temos as seguintes funções:

$f(x)=x^{2} -1$

$g(x)=x+2$

Calculando $f(g(x))$ :

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

Quando $f(g(x))=0$ :

$f(g(x))=0\\\\x^{2} +4x+3=0\\\\\Delta=4^{2}-4.1.3\\\\\Delta=16-12\\\\\Delta=4\\\\x'=\dfrac{-4+\sqrt{4} }{2.1}\\\\x'=\dfrac{-4+2}{2}\\\\x'=\dfrac{-2}{2}\\\\\boxed{x'=-1} \\\\x''=\dfrac{-4-\sqrt{4} }{2.1}\\\\x''=\dfrac{-4-2}{2}\\\\x''=\dfrac{-6}{2}\\\\\boxed{x''=-3}$

O conjunto solução é:

$\boxed{\boxed{S=\{-3,-1\}}}$