Question

Sendo f(x) = 2x - 10 e g(x)=x2-100 calcule x para que se tenha g(f(x)=0

alguem ajuda?​

Answer 1

Explicação passo-a-passo:

$\sf g(f(x))=g(2x-10)$

$\sf g(f(x))=(2x-10)^2-100$

$\sf (2x-10)^2-100=0$

$\sf (2x-10)^2=100$

$\sf 2x-10=\pm\sqrt{100}$

• $\sf 2x-10=10$

$\sf 2x=10+10$

$\sf 2x=20$

$\sf x=\dfrac{20}{2}$

$\sf x'=10$

• $\sf 2x-10=-10$

$\sf 2x=-10+10$

$\sf 2x=0$

$\sf x=\dfrac{0}{2}$

$\sf x"=0$

$\sf S=\{0,10\}$