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Among the following functions, which one is an EVEN function? (i) f(x) = x³ * sin(3x) (ii) f(x) = (e^(x²) + e^(-x²)) / (2x) (iii) f(x) = (e^x - e^(-x)) / (e^x + e^(-x)) (iv) f(x) = x² + 2^x

1. (i) only
2. (ii) only
3. (iii) only
4. (iv) only

Correct answer: (i) only

Solution

Checking each: (i) odd*odd = even; (ii) even/odd = odd; (iii) tanh-type is odd; (iv) has no symmetry due to 2^x. So only (i) is even.

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