First slide

Functions (XII)

Question

The domain of f(x) $= \frac{\log (\sin^{- 1} \sqrt{x^{2} + x + 1})}{\log (x^{2} - x + 1)}$ is

Moderate

A

(-1 , 1)
B

(-1 ,0) $\cup$ (0 , 1)
C

(-1 , 0) $\cup$ { 1}
D

None of these

Solution

Here , log ( x²-x+1) is defined , when
x²-x+1>0 and $x^{2} - x + 1 \neq 0$
$\Rightarrow x \in R and x \neq 0, 1 \Rightarrow x \in R - {0, 1}$
Again ,log (sin ^-1 $\sqrt{x^{2} + x + 1}$ ) exists , when
0< x²+x+1 $\leq$ 1
$\Rightarrow x^{2} + x \leq 0 \Rightarrow x \in [- 1, 0] x \in [- 1, 0]$

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