Edit: I missed part of the Question sorry. This should be correct now.
(f/g) = (x^2+2x+2) / (√5+x)
Start by assuming that the domain is all reals (-inf, inf). Then think about what restrictions there on on what x can be.
The Denominator cannot be zero. So √(5+x) cannot be 0.
Solve √(5+x)=0 for x to find what value(s) of x make the denominator zero. x = -5
Also, you cannot take the square root of a negative number. So (5+x) >(or =) 0.
If x is anything below -5, then 5+x will be negative. So x>-5
So the domain is everything above and including -5 EXCEPT -√5, or [-5, -√5) U (-√5, inf). You use parenthesis and not brackets because -√5 and is not in the domain, and you never put a bracket on + or - infinity.
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Edit: I missed part of the Question sorry. This should be correct now.
(f/g) = (x^2+2x+2) / (√5+x)
Start by assuming that the domain is all reals (-inf, inf). Then think about what restrictions there on on what x can be.
The Denominator cannot be zero. So √(5+x) cannot be 0.
Solve √(5+x)=0 for x to find what value(s) of x make the denominator zero. x = -5
Also, you cannot take the square root of a negative number. So (5+x) >(or =) 0.
If x is anything below -5, then 5+x will be negative. So x>-5
So the domain is everything above and including -5 EXCEPT -√5, or [-5, -√5) U (-√5, inf). You use parenthesis and not brackets because -√5 and is not in the domain, and you never put a bracket on + or - infinity.