Question

If f(x) = `{{:(4x - 2",", 0 ≤ x ≤ 2),(3x + "k"",", 2 < x ≤ 3):}` is continuous in [0, 3], then the value of k is ______.

Options

• –1

• 0

• –3

• –2

Answer 1

If f(x) = `{{:(4x - 2",", 0 ≤ x ≤ 2),(3x + "k"",", 2 < x ≤ 3):}` is continuous in [0, 3], then the value of k is 0.

Explanation:

Since, f(x) is continuous in [0, 3].

∴ It is continuous at x = 2.

⇒ `lim_(x -> 2^-) "f"(x) = lim_(x -> 2^+) "f"(x)` 

⇒ `lim_(x -> 2^-) (4x - 2) = lim_(x > 2^+) (3x + "k")`

⇒ 4(2) – 2 = 3(2) + k

⇒ 6 = 6 + k

⇒ k = 0