How do I find the domain of the following function?

Question

1/(x^2+1-x+21)

Answer 1

The domain is the values of x which can be used to find a y value or f(x) or whatever. In this case you are worried about a 0 in the denominator(Can't divide by 0) so we are going to make the equation:
0=x^2+1-x+21 simplify
0=x^2-x+22 solve
There are no solutions!
Therefore: The domain for this problem is all real numbers.

Answer 2

the domain is all real numbers except those that make
x^2+1-x+21 equal to zero.
because then 1 / ( x^2+1-x+21) becomes 1 / zero , and that is not defined.

so solve : x^2+1-x+21=0
R - solution is the domain.

Answer 3

usually domain means what values can x have.

since you can not have a 0 denominator, then the solution to the equation x^2+1-x+21=0 gives you the only values of x which are NOT in the domain.

x^2+1-x+21=x^2-x+22=0

by any chance is there a typo in your problem?

x^2-x+22=0
x^2-x+1/4=-22+1/4
(x-1/2)^2=-88/4+1/4=-87/4
x-1/2=+ or - sqrt(-87)/2
x=1/2+ or - sqrt(-87)/2
x=[1+sqrt(-87)]/2 and
x=[1-sqrt(-87)]/2
x is all real and complex numbers other than [1+sqrt(-87)]/2 and [1-sqrt(-87)]/2