If f(x)=|x| and g(x)=x², what is the nature of (fg)(x)?

Correct answer: Even function

The governing concept is the parity of a product of functions. Here (fg)(x) means f(x)g(x), so h(x)=(fg)(x)=|x|x². Both factors are even because |−x|=|x| and (−x)²=x². Direct substitution confirms this: h(−x)=|−x|(−x)²=|x|x²=h(x), which is precisely the definition of an even function. It is not odd, since an odd function must satisfy h(−x)=−h(x). Option D is not the correct classification: although h(x) is non-negative, it is zero at x=0, so it is not positive for every real x. Thus option A is correct.