Question

for the piece-wise function f(x)x^2 +k,if x<2 and f(x)=2xk,if x+2, determine which value of k makes f(x) continuous.

Answer 1

Answer:

$k = \frac{4}{3}$

Step-by-step explanation:

$f(x) = x² + k, x < 2$

$\:\:\:\:\:\:\:\:\:\:= 2xk , x ≥ 2$

f(x) will be continuous at x = 2 if

$lim_{x - > 2⁺}f(x) = lim_{x - > 2⁻}f(x) = f(2)$

⇒ 2² + k = 2*2k

⇒ 4 + k = 4k

⇒ 4 = 3k

$⇒ k = \frac{4}{3}$