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Nonlinear Functions

SAT Math· difficulty 4/5

If f(x)f(x) is even and g(x)g(x) is odd, what type of function is h(x)=f(x)+g(x)h(x) = f(x) + g(x) (assuming neither is zero)?

  • A

    Even

  • B

    Both

  • C

    Odd

  • D

    Neither

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Explanation

h(−x)=f(−x)+g(−x)=f(x)−g(x)h(-x) = f(-x) + g(-x) = f(x) - g(x), which is neither h(x)h(x) nor −h(x)-h(x).

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