Answer:
None of the options presented is the correct answer
Step-by-step explanation:
Composite Function
Given two functions u(x) and v(x), we call the composite function [tex](u\circ v)(x)[/tex] to the expression u(v(x)) and [tex](v\circ u)(x)[/tex]=v(u(x)).
We are given
[tex]u(x)=-2x^2[/tex]
[tex]\displaystyle v(x)=\frac{1}{x}[/tex]
LEt's compute the composite function
[tex]\displaystyle u(v(x))=-2(\frac{1}{x})^2[/tex]
[tex]\displaystyle u(v(x))=-\frac{2}{x^2}[/tex]
This function doesn't exist for x=0. For any other value of x, the denominator is always positive, and the function is always negative. When x tends to infinite (positive or negative), the function tends to zero. So the range of the composite function [tex](u\circ v)(x)[/tex] is [tex](-\infty,0)[/tex]
None of the options presented is the correct answer
