Question #757f2

1 Answer
Feb 24, 2017

Answer:

the domain is all the real vales of x, or: (−∞,∞)
the range is: #y≥1# or #[1,∞)#

Explanation:

#f(x)=sqrt(x^2+1)#
The domain:
A square root function is defined if where the entire statement under the radical sign is equal or greater than 0, so in this case:
#x^2+1>=0# => or:
#x^2>=-1#=> this is always true, hence the domain is all the real vales of #x#, or: #(-oo, oo)#
The range:
In its valid domain the absolute minimum value of #f(x)# occurs when #x=0#, therefore the range is:
#y>=1# or #[1, oo)#