Question

Given f(x) = x² +3 and g(x)=x²+x+3, which statement is true?

a. Both f(x) and g(x) are even.
b. Both f(x) and g(x) are odd.
c. f(x) is even and g(x) is odd.
d. None of these are true.

Answer 1

The statement that is true is option c. f(x) is even and g(x) is odd.

Step-by-step explanation:

The statement that is true is option c. f(x) is even and g(x) is odd.

An even function is one that satisfies the condition f(-x) = f(x), which means that if you replace x with -x in the function, the function remains the same. For f(x) = x² + 3, we have f(-x) = (-x)² + 3 = x² + 3 = f(x), so f(x) is even.

An odd function is one that satisfies the condition f(-x) = -f(x), which means that if you replace x with -x in the function, the function is negated. For g(x) = x² + x + 3, we have g(-x) = (-x)² + (-x) + 3 = x² - x + 3 = -g(x), so g(x) is odd.