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Nonlinear Functions

SAT Math· difficulty 5/5

The function ff is defined as f(x)=ax4+bx2f(x) = ax^4 + bx^2 for constants a,ba, b. Which statement must be true?

  • A

    ff is odd

  • B

    ff has an inverse

  • C

    ff is neither even nor odd

  • D

    ff is even

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Explanation

Both terms have even powers of xx, so f(−x)=a(−x)4+b(−x)2=ax4+bx2=f(x)f(-x) = a(-x)^4 + b(-x)^2 = ax^4 + bx^2 = f(x). ff is even.

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