Question

Which statements are true for the functions g(x) = ? and iz(x) = -xp? Check all that apply.

For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
(x) &h(x) for r=-1.
For positive values of x 9(x) & h(x).
For negative values of x, g(x) & h(x).

Answer 1

The first statement is true while the second, fourth, and fifth statements are false.

Step-by-step explanation:

The first statement is true: For any value of x, g(x) will always be greater than h(x). From the given information, we know that g(x) is represented by ?, while h(x) is represented by -xp. Since ? is always positive and -xp is always negative (for positive values of x), g(x) will always be greater than h(x).

The second statement is false: For any value of x, h(x) will not always be greater than g(x). As explained above, g(x) will always be greater than h(x).

For positive values of x, the fourth statement is true: For any positive value of x, g(x) will always be greater than h(x). This is because the negative sign in front of xp in the function iz(x) will make h(x) negative for positive values of x, while g(x) is always positive.

For negative values of x, the fifth statement is false: For negative values of x, g(x) will not always be greater than h(x). Since both g(x) and h(x) will be negative for negative values of x, h(x) could be greater than g(x) depending on the specific values of x.