f(x) = {[kx^2,x≥1][4,x<1] at x = 1

Question

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

\(f(x) = \begin{cases}kx^2&, \quad x≥1\\4 &, \quad x<1\\\end{cases} \) at x = 1

Answer 1

Given : 

f(x) is continuous at x = 1 

If f(x) to be continuous at x = 1,

then,

f(1)^– = f(1)⁺ = f(1)

⇒ k(1–0)² 

⇒ k ....(2) 

Since, 

f(x) is continuous at x = 1 & also 

from (1) & (2),

∴ k = 4