Which of the following functions is even?
Show the answer and explanation
Correct answer
B. f(x) = x^2 + 1
Principle or equation
A function f is even if f(-x) = f(x) for all x in its domain.
Why this answer is correct
Check each option: x^3 - x gives -x^3 + x, not equal; x^2 + 1 gives (-x)^2 + 1 = x^2 + 1, equal; 2^x gives 2^(-x), not equal; sin x gives -sin x, not equal.
Example
For f(x) = x^2, f(-2) = 4 = f(2).
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