Question

x belongs to (-6,3) then find the interval in which x^2 lies

Answer 1

Answer:

If belongs to  (-6,3),  then x² belongs to [0,36)

Step-by-step explanation:

Given,

x belongs to (-6,3)

To find,

The interval in which x² lies

Solution:

Given interval is (-6,3)

Let us split this interval into two

(-6,3) = (-6,0)+[0,3)

Let us the consider the first interval (-6,0)

All the elements in this interval are negative numbers, and we know that the square of a negative number is a positive number

We have for all the elements x belongs to (-6,0), x² belongs to the interval (0,36), since (-6)² = 36

If x belongs to (-6,0), x² belongs to the interval (0,36)

Again let us consider [0,3)

All the elements in this interval are positive numbers, and the square of a positive number is always a positive number.

If x belongs to[0,3), x² belongs to the interval [0,9)

∴ If belongs to  (-6,3), then x² belongs to either (0,36) or [0,9)

That is x² belongs to the union of (0,36) and  [0,9) = [0,36)

∴ If x belongs to  (-6,3),  then x² belongs to [0,36)

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