Question

Let $f(x)\{\begin{array}{ll}3x-4,& 0\le x\le 2\\ 2x+l,& 2<x\le 9\end{array}$
If f is continuous at $x=2$, then what is the value of $l$ ?

• A. 0
• B. 2
• C. -2
• D. -1

Answer 1

Answer: (C)

Given function is : $f(x)\{\begin{array}{ll}3x-4,& 0\le x\le 2\\ 2x+l,& 2<x\le 9\end{array}$
and also given that f (x) is continuous at x = 2
For a function to be continuous at a point LHL = RHL = Value of a function at that point. f (2) = 2
$\Rightarrow LHL:\underset{x\to 2}{\lim }(2x+l)=3(2)-4$
$\Rightarrow \underset{h\to 0}{\lim }\{2(+h)+l\}=6-4$
$\Rightarrow 4+l=2$
$\Rightarrow l=-2$