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The domain of definition of f(x) =(log2(...

The domain of definition of f(x) =`(log_2(x+2))/(x^2+3x+2)`

A

`R//{-1,-2}`

B

`(-2,infty)`

C

`R//{-1,-2,-3}`

D

`(-3,infty)//{-1,-2}`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=(log_(2)(x+3))/((x^(2)+3x+2))=(log_(2)(x+3))/((x+1)(x+2))`
For numerator, `x+3 gt 0`
`rArr x gt -3 " ...(i) " `
and for denominator, `(x+1)(x+2) ne 0`
` rArr x ne -1, -2 " ...(ii)" `
From Eqs. (i) and (ii) ,
Domain is `(-3,oo)//{-1,-2}`
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