Question

if x € (-2, 5) then find the interval in which
${x}^{2}$
lies​

Answer 1

first of all try yourself by help of examples dont be dependent on anyone in your exam no one will help you if then also you are anable to solve then ask me again and again till you do not understand how to solve

Answer 2

If x ∈ (-2, 5) then the interval in which $x^2$ lies​ is [0, 25).

Given,

A variable x ∈ (-2, 5).

To Find,

The interval in which $x^2$ lies.

Solution,

The method of finding the interval in which $x^2$ lies is as follows -

We can divide the interval into two parts in which x lies.

(-2, 5) = (-2, 0) ∪ [0, 5)

If x ∈ (-2, 0), then we can simply observe that $x^2$ ∈ (0, 4) since the square of a non-zero number is always greater than 0.

Also, if x ∈ [0, 5), we can simply tell that $x^2$ ∈ [0, 25).

So the union of the two sets is  (0, 4) ∪ [0, 25) = [0, 25).

Hence, if x ∈ (-2, 5) then the interval in which $x^2$ lies​ is [0, 25).

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