If g(x) is an odd function, which function must be an even function?

Since g is odd, g(−x) = −g(x). For the squared function, f(−x) = [g(−x)]² = [−g(x)]² = [g(x)]² = f(x), which is the defining property of an even function. Thus f(x) = g(x)² must be even.

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