CGPET 2015 Solved Paper

Given, f(x)=loge(6−|x2+x−6|)
The function f(x) is defined, if
(6−|x2+x−6|)>0
⇒ |x2+x−6|<6
⇒ −6<x2+x−6<6
If x2+x−6<6
⇒ x2+x−12<0
⇒ (x+4)(x−3)<0

∴ x∈(−4,3) ....(i)
⇒ x2+x>0⇒x(x+1)>0

∴ x∈(0,∞) ...(ii)
From Eqs. (i) and (ii), we get
x∈(0,3)
∵ f(x) has only two integral values.
∴ x=1,2