f(x) = {[k(x^2+2),if x ≤ 0][3x+1,if x > 0]at x = 0

Question

Find the value of the constant k so that the given function is continuous at the indicated point :

\(f(x) = \begin{cases}k(x^2+2)&, \quad{if}\, x≤0\\3x+1 &, \quad {if}\,x>0\\\end{cases} \)at x = 0

Answer 1

Given : 

f(x) is continuous at x = 0 

If f(x) to be continuous at x = 0,

then,

f(0)^– = f(0)⁺ = f(0)

⇒ k(0 + 2)

⇒ 2k ...(1)

⇒ 1 ...(2)

Since, 

f(x) is continuous at x = 0,

From (1) & (2),we get,

2k = 1

⇒ k = \(\frac{1}{2}\)