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Nonlinear Functions

SAT Math· difficulty 4/5

If h(x)=(3x+2)2h(x) = (3x + 2)^2, which expresses hh as a composition f(g(x))f(g(x))?

  • A

    f(x)=x2f(x) = x^2 and g(x)=3x+2g(x) = 3x + 2

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  • B

    f(x)=(x+2)2f(x) = (x + 2)^2 and g(x)=3xg(x) = 3x

  • C

    f(x)=x2+2f(x) = x^2 + 2 and g(x)=3xg(x) = 3x

  • D

    f(x)=3x+2f(x) = 3x + 2 and g(x)=x2g(x) = x^2

Explanation

With g(x)=3x+2g(x) = 3x + 2 inside and f(x)=x2f(x) = x^2 outside, f(g(x))=(3x+2)2=h(x)f(g(x)) = (3x + 2)^2 = h(x).

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