Which statements are true for the functions g(x) = x^2 and h(x) = –x^2 ? Check all that apply.A.For any value of x, g(x) will always be greater than h(x).B.For any value of x, h(x) will always be greater than g(x).C.g(x) > h(x) for x = -1. D.g(x) < h(x) for x = 3. E.For positive values of x, g(x) > h(x). F.For negative values of x, g(x) > h(x)

Answer:C, E, FStep-by-step explanation:The range of the function [tex]g(x)=x^2[/tex] is [tex]y\in [0,\infty)[/tex], the range of the function [tex]h(x)=-x^2[/tex] is [tex](-\infty,0][/tex]This means that for any value of x, the value of [tex]g(x)[/tex] is always greater or equal to the value of [tex]h(x)[/tex] (the values are equal at x=0).So, options A and B are false, because at x=0 the values are equal and h(x) cannot be greater than g(x)Options C, E and F are true, because for all non-zero x, g(x)>h(x).Option D is false (the reason is the same as for option B)