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Given f(x)=(x(x-p))/(q-p)+(x(x-q))/(p-q), where p≠ q, determine the value of f(p)+f(q).

1. f(p-q)
2. f(p+q)
3. f(p(p+q))
4. f(q(p-q))

Correct answer: f(p+q)

Solution

Combining the terms, f(x) = x(x-p)/(q-p) + x(x-q)/(p-q) simplifies to f(x) = x. Hence f(p)+f(q) = p+q = f(p+q).

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