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

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Answer 1 · 2018-02-01T06:26:22

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

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]}