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If f(x)=√(1+x²), then which of the following statements is true?

1. f(xy)=f(x) f(y)
2. f(xy)≥ f(x) f(y)
3. f(xy)≤ f(x) f(y)
4. None of these

Correct answer: f(xy)≤ f(x) f(y)

Solution

f(x)f(y)=sqrt((1+x^2)(1+y^2))=sqrt(1+x^2+y^2+x^2y^2), while f(xy)=sqrt(1+x^2y^2). Since x^2+y^2>=0, we always have f(xy) <= f(x)f(y).

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