Question #7fcf8

1 Answer
Yiu A.
Oct 24, 2017

#(-oo,oo)#

Explanation:

There's no constrain to the domain of the question. So, #x# can be any real number. Domain#=(-oo,oo)#

Here is some case that there are constrains:
1.
squareroot : #sqrt(x^2+5x+6)#
As the things inside squareroot cannot be -ve, #x^2+5x+6# have to be greater than or equal to #0#.

#x^2+5x+6>=0#
#(x+5)(x+1)>=0#
#x<=-5 or x>=-1#

The domain#= (-oo,-5]U[-1,oo)#

2.
ln / log: #ln(x^2+5x+6)#
As the things inside ln can only be +ve, #x^2+5x+6# have to be greater than #0#.

#x^2+5x+6>0#
#(x+5)(x+1)>0#
#x<-5 or x>-1#

The domain#= (-oo,-5)U(-1,oo)#

3.
fraction: #(x^2+5x+6)/(x-2)#
As the denominator of the fraction cannot equal to #0#,
#x-2!=0#
#x!=2#

The domain#= (-oo,2)U(2,oo)#

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