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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

Text Solution

Verified by Experts

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