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Given f(x)=(ax+b)/(x+1), lim(x to oo)f(x...

Given `f(x)=(ax+b)/(x+1), lim_(x to oo)f(x)=1 and lim_(x to 0)f(x)=2`, then f(-2) is

A

0

B

1

C

2

D

3

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The correct Answer is:
A
Given `lim_(x to oo)""f(x)=1`
`lim_(x to oo)""(ax+b)/(x +1)=1 `
`implies lim_(x to oo)""(a+(b)/(x))/(1+(1)/(x))=1 `
`implies a=1 `
Also , `lim_(x to oo)f(x)=2 `
`implies lim_(x to oo)""(ax+b)/(x+1)=2 `
` implies b=2 `
Now , f(-2)=`(a(-2)+b)/((-2)+1)=(-2+2)/(-2+1)=0`
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