Question

If $f(x) = \begin{cases} 3x - 2, & 0 \leq x \leq 1\\ 2x^2 + ax, & 1<x<2 \end{cases}$ is continuous for $x \in (0, 2)$, then $a$ is equal to :

• A. -4
• B. -7
• C. -2
• D. -1

Hint:

For continuity at a point, equate the left-hand and right-hand limits at that point.

Answer 1

The Correct Option is B

For continuity at $x = 1$, the left-hand limit must equal the right-hand limit. The left-hand limit is: \[f(1) = 3(1) - 2 = 1\] The right-hand limit is: \[f(1) = 2(1)^2 + a(1) = 2 + a\] Equating these limits: \[1 = 2 + a \quad \Rightarrow \quad a = -1\] Therefore, $a = -1$.