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If the function f(x)=(3x^2+ax+a+3)/(x^2+...

If the function `f(x)=(3x^2+ax+a+3)/(x^2+x-2)` is continuous at `x=-2,` then the value of `f(-2)` is

A

0

B

`-1`

C

1

D

2

Text Solution

Verified by Experts

The correct Answer is:
B
Since the function is continuous at `x=-2`, then
`f(-2)=underset(xrarr-2)(lim)f(x)`
`" "=underset(xrarr-2)(lim)(3x^(2)+ax+a+3)/(x^(2)+x-2)`
this limit will exist if `15-a=0`
`rArr" "a=15" (i)"`
So, `" "underset(xrarr-2)(lim)f(x)=underset(xrarr-2)(lim)(3x^(2)+15x+18)/(x^(2)+x-2)`
`" "=underset(xrarr-2)(lim)(3(x+2)(x+3))/((x+2)(x-1))`
`" "=underset(xrarr-2)(lim)(3(x+3))/((x-1))`
`" "=(3)/(-3)=-1`
Hence, `f(-2)=-1`
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