Question

Determinar os domínios das funções abaixo:

(a) f(x) = 3x + 2/ײ − 49

(b) f(x) =√3x − 24

(c) h(x) = ³√17x²+ 19x − 2016​

Answer 1

a)

$f(x)=3x+\dfrac{2}{x^2}-49\\\\ x^2\neq0\ \therefore\ x\neq0\\\\ \boxed{\mathbb{D}=\mathbb{R}-\left\{0\right\}}$

b)

$f(x)=\sqrt{3x-24}\\\\ 3x-24\geq0\ \therefore\ x\geq\dfrac{24}{3}\ \therefore\ x\geq8\\\\ \boxed{\mathbb{D}=[8,\infty)}$

c)

$h(x)=\sqrt[3]{17x^2+19x-2016}\\\\ \boxed{\mathbb{D}=\mathbb{R}=(-\infty,\infty)}$