Show that f(x)=1 x is decreasing function on (0, ). - Vidyadip

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.

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