If r(x) = 2 – x2 and w(x) = x – 2, what is the range of (Wºr) (x)(-∞,0](-∞,2][0,∞)[2,∞)

Answer:(-inf,2]Step-by-step explanation:[tex](w \circ r)(x)=w(r(x))[/tex][tex]w(2-x^2)[/tex] I replaced r(x) with 2-x^2[tex](2-x^2)-x[/tex] I replace the x in w(x)=x-2 with 2-x^2[tex]-x^2-x+2[/tex]You can graph this to find the range.But since this is a quadratic (the graph is a parabola), I'm going to find the vertex to help me to determine the range.The vertex is at x=-b/(2a).  Once I find x, I can find the y that corresponds to it by using y=-x^2-x+2.Comparing ax^2+bx+c to -x^2-x+2 tells me a=-1, b=-1, and c=2.So the vertex is at x=1/(2*-1)=-1/2.To find the y-coordinate that corresponds to that I will not plug in -1/2 in place of x into -x^2-x+2.This gives me -(-1/2)^2-(-1/2)+2-1/4 +  1/2  +2Find a common denominator which is 4.-1/4 +  2/4  +8/48/42.So the highest y value is 2 ( I know tha parabola is upside down because a=negative number)That mean then range is 2 or less than 2.So the answer an interval notation is (-inf,2]