If `f(x)=(x^(2)-9)/(x^(2)-2x-3),xne3` is continuous at x=3, then which one of the following is correct?

Options

A. f(3)=0
B. f(3)=1.5
C. f(3)=3
D. f(3)=-1.5

Answer

B

Explanation

`f(x)=(x^(2)-9)/(x^(2)-2x-3)`
Given, the function is continuous at x=3.
`f(3)=underset(xto3)lim(x^(2)-9)/(x^(2)-2x-3)`
`f(3)=underset(xto3)lim((x^(2)+3)(x-3))/((x-3)(x+1))`
`=(3+3)/(3+1)=(6)/(4)=(3)/(2)=1.5`.