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The function \(f(x)=(1 / 2)^x\) on \(R\) is
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Strictly decreasing
Let \(y=\left(\frac{1}{2}\right)^x\) on \(R\)
\(\frac{d y}{d x}=\left(\frac{1}{2}\right)^x \log \frac{1}{2}=-\left(\frac{1}{2}\right)^x \log 2\)
\(\left(\frac{d y}{d x} < 0\right)\) so strictly decreasing
\(\frac{d y}{d x}=\left(\frac{1}{2}\right)^x \log \frac{1}{2}=-\left(\frac{1}{2}\right)^x \log 2\)
\(\left(\frac{d y}{d x} < 0\right)\) so strictly decreasing
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