Question

For what value of k will the function f be continuous on (−∞, ∞)?

f(x) =

x + 3 if x ≤ 1
kx2 if x > 1

Answer 1

4

(Hopefully x2 means x^2. That's what I read it as.)

Explanation:

We need the relation to match the same number on both sides at x=1.

So we need

x+3=kx^2 for x=1

1+3=k(1)^2

4=k

The function is continuous when k=4.