Can someone help me solve this math problem?

Question

Find c so that both functions are continuous.

(x + 3), x is less than/equal 2
(cx + 6), x is greater than 2

Answer 1

at 2, your first function is 5. That is where your second function needs to start, so set (cx+6)=5 with x=2.

Then 2c+6=5 2c=-1 c=-1/2

Answer 2

It is continuous for any c when x =/= 2. In order for it to be continuous lim (x ->2+0) x+3 = lim (x -> 2-0) cx + 6

Plug x=2 into both and get

2+3 = 2c + 6

5 = 2c + 6

2c = -1

c = -1/2