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Nonlinear Functions

SAT Math· difficulty 5/5

For all x≥1x \geq 1, which is correct?

  • A

    x≤x≤x2≤2x\sqrt{x} \leq x \leq x^2 \leq 2^x for sufficiently large xx

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  • B

    x≤xx \leq \sqrt{x} always

  • C

    2x≤x2^x \leq x always

  • D

    x2≥2xx^2 \geq 2^x always

Explanation

Growth ordering for large xx: x≤x≤x2≤2x\sqrt{x} \le x \le x^2 \le 2^x.

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