Find the domain of the following i f x - - x2- - 1 - -3 - - x2-

√([ x ^ 2 ] 1 ) + √( 3 [ x ^ 2 ] ) ⇒ [ x ^ 2 ] 1≥ 0 + 3 [ x ^ 2 ] ≥ 0 ⇒ x ∈ ( ∞ , 1 ] ∪ [ 1,0 ) f x ∈ [ √( 3 ) , √( 3 ...

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Standard XII

Mathematics

Definition of Functions

Find the doma...

Question

Find the domain of the following
(i) $f (x) = \sqrt{[x^{2}] - 1} + \sqrt{3 - [x^{2}]}$

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Solution

$\sqrt{[x^{2}] - 1} + \sqrt{3 - [x^{2}]}$

$\Rightarrow [x^{2}] - 1 \geq 0 + 3 - [x^{2}] \geq 0$

$\Rightarrow x \in (- \infty, - 1] \cup [1, 0)$

$f x \in [- \sqrt{3}, \sqrt{3}]$

$\Rightarrow x \in [\sqrt{3}, \infty)$

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Find the domain of the following (i)f(x)=√[x2]−1+√3−[x2]

√[x2]−1+√3−[x2]⇒[x2]−1≥0+3−[x2]≥0⇒x∈(−∞,−1]∪[1,0)fx∈[−√3,√3]⇒x∈[√3,∞)

Find the domain of the following
(i) $f (x) = \sqrt{[x^{2}] - 1} + \sqrt{3 - [x^{2}]}$

$\sqrt{[x^{2}] - 1} + \sqrt{3 - [x^{2}]}$

$\Rightarrow [x^{2}] - 1 \geq 0 + 3 - [x^{2}] \geq 0$

$\Rightarrow x \in (- \infty, - 1] \cup [1, 0)$

$f x \in [- \sqrt{3}, \sqrt{3}]$

$\Rightarrow x \in [\sqrt{3}, \infty)$