The function \(f(x)=(1 / 2)^x\) on \(R\) is

The function \(f(x)=(1 / 2)^x\) on \(R\) is
  1. Strictly decreasing
  2. Strictly increasing
  3. Decreasing
  4. Neither increasing nor decreasing

Solution

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

Asked in: AP EAMCET 2020 (17 Sep Shift 1)

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