Question

If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (w circle r) (x)?

(negative infinity, 0 right-bracket

(negative infinity, 2 right-bracket

Left-bracket 0, infinity)

Left-bracket 2, infinity)

Answer 1

Answer:

$(-\infty, 0)$

Step-by-step explanation:

(w circle r) (x) is the composite function(w of r(x)), that is, w(r(x))[/tex]

We have that:

$r(x) = 2 - x^{2}$

$w(x) = x - 2$

Composite function:

$w(r(x)) = w(2 - x^{2}} = 2 - x^{2} - 2 = -x^{2}$

$-x^{2}$ is a negative parabola with vertex at the original.

So the range(the values that y assumes), is:

$(-\infty, 0)$

Answer 2

The range of (w circle r) (x) will be (-∞,0). Option A is correct.

What is a function?

A connection between independent variables and the dependent variable is defined by the function.

Functions help to represent graphs and equations. A function is represented by the two variables one is dependent and another one is an independent function.

The relation between them is shown as y if dependent and x is the independent variable;

Given functions;

$\rm r(x) =2- x^2 \\\\ w(x) =x-2$

The composite function is found as;

$\rm w(r(x))=w(2-x^2 = 2-x^2-2)\\\\ w(r(x))= -x^2$

-x² is graphed and shows the negative parabola

The range of (w circle r) (x) will be (-∞,0).

Hence, option A is correct.

To learn more about the function refer to the link https://brainly.com/question/12431044.

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