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Nonlinear Functions

SAT Math· difficulty 4/5

If f(x)=x2f(x) = x^2 and g(x)=x+5g(x) = \sqrt{x + 5}, what is the domain of f(g(x))f(g(x))?

  • A

    x≥5x \geq 5

  • B

    All real numbers

  • C

    x≥−5x \geq -5

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  • D

    x≥0x \geq 0

Explanation

g(x)=x+5g(x) = \sqrt{x + 5} requires x+5≥0x + 5 \geq 0, i.e., x≥−5x \geq -5.

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