First slide

Functions (XII)

Question

The domain of f(x)=log _x+3( $x^{2} - 1$ )

Moderate

A

1.(-3,-1) $\cup$ (1, $\infty$ )
B

2.[-3,-1) $\cup$ [1, $\infty$ )
C

3.(-3,-2) $\cup$ (-2,-1) $\cup$ (1, $\infty$ )
D

4. none of these

Solution

Given f(x)=log _x+3( $x^{2} - 1$ )
f(x) is to be defined, when x²-1>0,3+x>0 and 3+x $\neq$ 1
i.e x²>1,x>-3 and x $\neq$ -2
i.e x< -1 or x>1,x>-3 and x $\neq$ -2
$∴$ Domain =(-3,-2) $\cup$ $(- 2, - 1) \cup (1, \infty)$

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