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If y=f(x)=((x+3))/((x-1)),t h e n x=f(y...

If `y=f(x)=((x+3))/((x-1)),t h e n` `x=f(y)` (b) `f(1)=3` `y` increases with `xforx<1` `f` is a rational function of `x`

A

x = f(y)

B

f(1) = 3

C

y increase with x for x lt 1

D

f is a rational function of x

Text Solution

Verified by Experts

The correct Answer is:
A, D
Given, `y=f(x)=(x+2)/(x-1)`
`rArr yx-y=x+2 rArr x(y-1) = y+2`
`rArr x=(y+2)/(y-1) rArr x=f(y)`
Here, f(1) does not exist, so domain ` in R-{1}`
`(dy)/(dx)=((x-1)*1-(x+2)*1)/((x-1)^(2))`
`= -(3)/((x-1)^(2))`
`rArr` f(x) is decreasing for all ` x in R -{1}.`
Also, f is rational function of x.
Hence, (a) and (d) are correct options.
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