Respuesta :

Answer:

(−∞, 0) ∪ (0, ∞)

Step-by-step explanation:

Given :

u(x) = -2x²

[tex]V(x)=\sqrt{\frac{1}{x} }[/tex]

Determining UoV(x) :

[tex]UoV(x)=U(V(x))=-2\left( \sqrt{\frac{1}{x} } \right)^{2}[/tex]

Then

[tex]UoV(x)=U(V(x))=-2 \times \frac{1}{x}[/tex]

Then

[tex]UoV(x)=U(V(x))=- \frac{2}{x}[/tex]

Since the range of  -2/x  is all real numbers except zero

Then

The range of UoV is :

(−∞, 0) ∪ (0, ∞)