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Find the domain and the range of the re...

Find the domain and the range of the real function f defined by `f(x)=sqrt((x-1))`.

A

Domain`=(1,oo),` Range `= (0,oo)`

B

Domain`=[1,oo),` Range `= (0,oo)`

C

Domain`=(1,oo),` Range `= [0,oo)`

D

Domain`=[1,oo),` Range `= [0,oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
We have, `f(x)=sqrt(x-1)`
f(x) is defined if, `x-1ge0`.
`rArr xge1`
`:.` Domain of `f=[1,oo)`
Let f(x)=y
`:. y=sqrt(x-1)`
`rArr y^(2)=x-1`
`:. x=y^(2)+1`
x assumes real values for `y in R.`
but `yge0`
`:.` Range of `f=[0,oo)`
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