Question

class 11 inequalities Find the range of value of the reciprocal of x when x belongs to [-3,5]​

Answer 1

-3 ≤ x ≤ 5

taking reciprocal

1/-3 ≥ x ≥ 1/5

1/5 ≤ x ≤ -1/3

Range of value = $\sf \bigg[ \frac{1}{5} , \: - \frac{1}{3} \bigg]$

Answer 2

The range of reciprocal of x is (-∞, -1/3] ? [1/5, ∞)

Step-by-step explanation:

Reciprocal of x is 1/x

Given

$-3\le x\le 5$

Case I

If $-3\le x<0$

Then

$-\frac{1}{3}\ge \frac{1}{x}>\infty$

or, $\infty<\frac{1}{x}<-\frac{1}{3}$

Case II

If $0< x\le 5$

Then

$\infty>\frac{1}{x}\ge\frac{1}{5}$

or, $\frac{1}{5}\le \frac{1}{x}\le \infty$

Case III

At x = 0, 1/x is not defined

Therefore, the range of reciprocal of x is

x ∈ (-∞, -1/3] ? [1/5, ∞)

Hope this answer is helpful.

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