What is the domain and range of $f (x) = \frac{1}{1 + \sqrt{x}}$ $f(x) = 1/(1 + sqrtx)$ ?

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Answer 1 · 2018-02-01T06:26:22

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

What's under the square root sign is $\geq 0$ $>=0$

Therefore,

$x \geq 0$ $x>=0$

So , the domain is $x \in [0, + \infty)$ $x in [0, +oo)$

To calculate the range, proceed as follows :

Let $y = \frac{1}{1 + \sqrt{x}}$ $y=1/(1+sqrtx)$

When $x = 0$ $x=0$ , $\Rightarrow$ $=>$ , $y = 1$ $y=1$

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]}

What is the domain and range of f(x) = 1/(1 + sqrtx)f(x)=11+√xf(x) = 1/(1 + sqrtx)?