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4-22.

Is f(x) = xsin(x) even, odd or neither?

f(a) = asin(a)
f(−a) = −asin(−a)
but, since y = sinx is odd,
= −a(−sin(a)) = asin(a)
So f(a) = f(−a)
therefore, y = xsinx is even.

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