Question

If r(X)=2-x^2 and w(X)=X-2, what is the range of (w*r)(X)

A) (-infinity,0]

B) (-infinity,2]

C) [0,infinity)

D) [2,infinity)

Answer 1

The range of (w*r)(X) is (-infinity, -2] U [0, infinity).

Step-by-step explanation:

To find the range of (w*r)(X), we need to find the range of the function w*r. The range of a function is the set of all possible values of the output variable.

The function (w*r)(X) is obtained by multiplying the functions w(X) and r(X). So, we need to first find the range of w(X) and then find the range of r(X). Finally, we need to find the range of the product of these two ranges.

The range of w(X) is the set of all possible values that X-2 can take. Since there are no restrictions on X, the range of w(X) is (-infinity, infinity).

The range of r(X) is the set of all possible values that 2-x^2 can take. The maximum value of 2-x^2 occurs at x=0 and is 2. So, the range of r(X) is (-infinity, 2].

Now, to find the range of (w*r)(X), we need to find the product of the two ranges. The product of (-infinity, infinity) and (-infinity, 2] is (-infinity, -2] U [0, infinity). Therefore, the range of (w*r)(X) is (-infinity, -2] U [0, infinity).

Answer 2

answer is a on e2020