If , then the range of…

MATHEMATICS · Single correct · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

If f(x)=π(x+7−4x−9)f(x)=\pi\left(\frac{\sqrt{x+7}-4}{x-9}\right), then the range of y=sin⁡(2f(x))y=\sin(2f(x)) is (a) [0,1][0,1] (b) (0,12]\left(0,\frac{1}{\sqrt2}\right] (c) (0,12)∪(12,1]\left(0,\frac{1}{\sqrt2}\right)\cup\left(\frac{1}{\sqrt2},1\right] (d) (0,1](0,1]

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