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The domain of the definition of the func...

The domain of the definition of the function
`f(x)=(1)/(4-x^(2))+log_(10)(x^(3)-x)` is

A

`(-1,0) cup (1,2) cup (3 ,infty)`

B

`(-2,-1) cup (-1,0) cup (2,infty)`

C

`(-1,0) cup (1,2) cup (2,infty)`

D

`(1,2) cup (2,infty)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given function `f(x)=(1)/(4-x^(2))+log_(10)(x^(3)-x)`
For domain of of f(x)
`4-x^(2)ne 0 rArr x ne pm 2 " …(i)" `
`and x^(3)-x gt 0`
` rArr x(x-1)(x+1) gt 0`
From Wavy curve method,

` x in (-1,0) cup (1,infty) " ...(ii)" `
From Eqs. (i) and (ii), we get the domain of f(x) as `(-1,0) cup (1,2) cup(2, infty).`
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