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Let f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)...

Let `f(x)=(sqrt(x-2sqrt(x-1)))/(sqrt(x-1)-1)xdot` Then `f^(prime)(10=1` `f^(prime)(3/2)=-1` `dom a inoff(x)i sxgeq1` range of `f(x)i s(-2-1)uu(2,oo)`

A

`f(10)=1`

B

`f'(3//2)=-1`

C

domain of `f(x) is x ge 1`

D

range of `f(x) is (-2, -1)] cup (2,00)`

Text Solution

Verified by Experts

`f(x)(sqrt((x-1)^(2))+1-2sqrt(x-1))/(sqrt(x-1)-1)`
`=(|sqrt(x-1)-1|)/(sqrt(x-1)-1)x`
`={{:(-x",", if x in [1,2)),(x",", if x in (2,oo)):}`
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CENGAGE-DIFFERENTIATION-Exercise (Multiple)
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