Question

Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? 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 1

the answer is E...e is the answer

Answer 2

Answer:

Statement(C), Statement(E) and Statement(F) are true.

Step-by-step explanation:

Given,

$g(x)=x^2\\h(x)=-x^2$

Statement(A):

As we can see that for any real value of$x$, the value of$g(x)$ is always positive and the value of$h(x)$ is always negative.

But if the value of$x$ is imaginary than the given statement is False.

Statement(B):

If we take the imaginary value of$x$ then the given statement may satisfied.

But for the real values of the$x$, the given statement is False.

Statement(C):

$For \;x=-1:\\g(x)=1\;and\;h(x)=-1$

By which it is clear that:

$g(x)>h(x)$

So the given statement is true.

Statement(D):

$For \;x=3:\\g(x)=9\;and\;h(x)=-9$

By which it is clear that:

$g(x)>h(x)$

So the given statement is False.

Statement(E):

For the positive values of $x$:

$g(x)$ is always be positive and $h(x)$ is always be negative.

By which it is clear that:

$g(x)>h(x)$

So the given statement is true.

Statement(F):

For the negative values of $x$:

$g(x)$ is always be positive and$h(x)$ is always be negative.

By which it is clear that:

$g(x)>h(x)$

So the given statement is true.