Question

Let $ f(x) \begin{cases} 3x - 4 , &0 \leq x \leq 2 \\ 2x + l ,& 2 < x \leq 9 \end{cases}$
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{cases} 3x - 4 , &0 \leq x \leq 2 \\ 2x + l ,& 2 < x \leq 9 \end{cases}$
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
$\Rightarrow \:\: LHL : \displaystyle\lim_{x \to 2} (2x + l) = 3(2) - 4$
$\Rightarrow \:\: \displaystyle\lim_{h \to 0} \{2( +h)+l\} = 6 - 4$
$\Rightarrow \:\: 4 + l = 2$
$\Rightarrow \:\: l = - 2$