Question

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)`

Answer 1

Correct Answer - 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).`