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Linear Functions

SAT Math· difficulty 4/5

If f(x)=4x−3f(x) = 4x - 3 and g(x)=(x+3)/4g(x) = (x + 3)/4, which is true for all xx?

  • A

    f(g(x))=4xf(g(x)) = 4x

  • B

    f(g(x))=x+1f(g(x)) = x + 1

  • C

    f(g(x))=xf(g(x)) = x

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  • D

    f(g(x))=x−1f(g(x)) = x - 1

Explanation

f(g(x))=4⋅x+34−3=(x+3)−3=xf(g(x)) = 4 \cdot \frac{x+3}{4} - 3 = (x + 3) - 3 = x. (gg is the inverse of ff.)

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