if f(x) = (xm + 9)2, which statement about f(x) is true?

a. f(x) is an even function for all values of m.

b. f(x) is an even function for all even values of m.

c. f(x) is an odd function for all values of m.

d. f(x) is an odd function for all odd values of m.

The answer is B) f(x) is an even function for all even values of m.

A. f(x) is an even function for all values of m.

B. f(x) is an even function for all even values of m.

Step-by-step explanation:

f(x) is even for all values of x as a result of the 2 which is used to multiply the result of the expression xm +9. The product of 2 with any integer (even or odd) is even. As such, irrespective of the value of m and by extension  xm and xm + 9, f(x) will still be even as the result of xm + 9 will be multiplied by 2 to get the value of f(x).

For example, assume x = 1 and m = 1, then

f(1) = (1×1 + 9)2

f(1) = (1 + 9)2

= 20 (an even number)

furthermore, assume x = 1 and m = 2

f(1) = (1×2 + 9)2

f(1) = (2 + 9)2

= 22 (an even number)

Based on the explanation above, Options A and B are true.