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Nonlinear Functions

SAT Math· difficulty 5/5

If ff is odd and gg is odd, what type of function is h(x)=f(x)⋅g(x)h(x) = f(x) \cdot g(x)?

  • A

    Both

  • B

    Neither

  • C

    Odd

  • D

    Even

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Explanation

h(−x)=f(−x)⋅g(−x)=(−f(x))(−g(x))=f(x)g(x)=h(x)h(-x) = f(-x) \cdot g(-x) = (-f(x))(-g(x)) = f(x) g(x) = h(x). So hh is even.

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