First slide

Functions (XII)

Question

The domain of the function $f (x) = \cot^{- 1} (\frac{x}{\sqrt{x^{2} - [x^{2}]}}), x \in R is$

Moderate

A

$R - {\pm \sqrt{n}, n \in N}$
B

$R - {\sqrt{n}, n \geq 0, n \in I}$
C

R
D

R – {0}

Solution

Domain of cot^–1x is R and $\frac{x}{\sqrt{x^{2} - [x^{2}]}}$ is defined if x² ≠ [x²] (∵ x² ≥ [x²])
⇒ x ≠ 0 or +ve integer.
Hence, domain $= R - {\sqrt{n} : n \geq 0, n \in Z}$

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