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If the function f:R to R given by f...

If the function `f:R to R ` given by
`f(x)={(x+a"," , "if "x le 1),(3-x^(2)",","if " x gt1):}` is continuous at x = 1, then a is equal to

A

4

B

3

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
`LHL=lim_(x to 1^(-))f(x)=lim_(h to 0)(1-h+a)=1+a`
`RHL=lim_(x to 1^(+))f(x)=lim_(h to 0){3-(1+h)^(2)}=2`
For f(x) to be continuous, LHL=RHL
`rArr 1+a=2 rArr a =1`
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