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Linear Functions

SAT Math· difficulty 4/5

Let f(x)=2x+3f(x) = 2x + 3, g(x)=x−1g(x) = x - 1, and h(x)=f(g(x))h(x) = f(g(x)). What is h−1(x)h^{-1}(x)?

  • A

    x+32\dfrac{x + 3}{2}

  • B

    x−12\dfrac{x - 1}{2}

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  • C

    x+12\dfrac{x + 1}{2}

  • D

    2x−12x - 1

Explanation

h(x)=2(x−1)+3=2x+1h(x) = 2(x - 1) + 3 = 2x + 1. h−1(x)=(x−1)/2h^{-1}(x) = (x - 1)/2.

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