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If $$x\leq3$$, then find the interval between which the value of $$\dfrac{1}{x}$$ lies.

Note by Sahba Hasan
9 months, 2 weeks ago

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Suppose $$x > 0$$.
Then $$x \leq 3 \Rightarrow \frac{1}{x} \geq \frac{1}{3}$$ (on dividing by x).
This means $$\frac{1}{x} \in [\frac{1}{3}, \infty)$$.

If $$x < 0$$ then $$\frac{1}{x} \in (-\infty, 0)$$. (Look at the graph!).
$$\frac{1}{x}$$ is not defined at $$x = 0$$.

Combining all this we have $$\frac{1}{x} \in (-\infty, 0)\cup [\frac{1}{3}, \infty)$$. · 9 months, 2 weeks ago