Question

What is the domain and range of `f(x) = 1/(1 + sqrtx)`?

Answer 1

The domain is `x in [0, +oo)` and the range is `(0,1]`

Explanation:

What's under the square root sign is `>=0`

Therefore,

`x>=0`

So , the domain is `x in [0, +oo)`

To calculate the range, proceed as follows :

Let `y=1/(1+sqrtx)`

When `x=0`, `=>`, `y=1`

And

`lim_(->+oo)1/(1+sqrtx)=0^+`

Therefore the range is `(0,1]`

graph{1/(1+sqrtx) [-2.145, 11.9, -3.52, 3.5]}