Find the values of x for which expressio

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

Find the values of x for which expression $\sqrt{1-\sqrt{1-\sqrt{1-x^2}}}$ is meaningful.

Options:

[-1, 1]

[1, 0]

[1, 2]

(1, 1)

Correct Answer:

[-1, 1]

Explanation:

$\sqrt{1-\sqrt{1-\sqrt{1-x^2}}}$ is meaningful if

$1-\sqrt{1-\sqrt{1-x^2}}≥0$

or $\sqrt{1-\sqrt{1-x^2}}≤1$

or $1-\sqrt{1-x^2}≤1$

or $\sqrt{1-x^2}≥0$

or $1-x^2≥0$

or $x^2≤1$ or $x∈[-1, 1]$