Question
Show that $\text{f}(\text{x})=\frac{1}{\text{x}}$ is decreasing function on $(0,\infty).$
✓
Answer
We have, $\text{f}(\text{x})=\frac{1}{\text{x}}$ Let, $\text{x}_1,\text{x}_2\in(0,\infty)$ and $\text{x}_1>\text{x}_2$$\Rightarrow\frac{1}{\text{x}_1}<\frac{1}{\text{x}_2}$
$\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2)$ Thus, $\text{x}_1>\text{x}_2\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2)$ So, f(x) is decreasing function.
$\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2)$ Thus, $\text{x}_1>\text{x}_2\Rightarrow\text{f}(\text{x}_1)<\text{f}(\text{x}_2)$ So, f(x) is decreasing function.
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