Question

Question #7fcf8

Answer 1

`(-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)`