Question

Question #757f2

Answer 1

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)`