Answer:
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.
