If f(x)=x²+3x and g(x)=x²−3x, what is the nature of (f+g)(x)?

Correct answer: Even function

The governing concept is determining the parity of a function after performing algebraic operations on functions. Add the expressions term by term: (f+g)(x)=(x²+3x)+(x²−3x)=2x², because the linear terms +3x and −3x cancel. Let h(x)=2x². Then h(−x)=2(−x)²=2x²=h(x), which satisfies the definition of an even function. It is not odd, since an odd function would require h(−x)=−h(x); for example, h(1)=2 and h(−1)=2 rather than −2. It is not constant because h(0)=0 while h(1)=2. Therefore option A is the only correct classification. The cancellation of the opposite linear terms is the key algebraic step.