Domain and Range

To  have  a domain of all real numbers, the denominator cannot evaluate  to  0 for any real x

Therefore.....the  discriminant  must  be  <  0   for  the polynomial in the  denominator

So

4^2   - 4 (1)c  <  0

16  - 4c  < 0

16  <   4c

16/4 <   c

c  > 4

Therefore  c  = 5      is the smallest  integer  value  of  c   that guarantees  a  domain of all reals

What a clever little Claire.

You get all your homework done for you and you don't have to learn a thing.