Determine so that the function is continuous everywhere fx

Determine so that the function is continuous everywhere. f(x) = {x + 3 if x lessthanorequalto 2 cx + 6 if x > 2

Solution

The key point here is x = 2...

Basically, both x + 3 and cx + 6 being linear polynomials are continuous everywhere.

The main point wher we gotta check continuity is x = 2

When x = 2, x + 3 ---> 2 + 3 ----> 5
When x = 2 ---> cx + 6 ----> 2c + 6

For it to be continuous at x = 2, we have :
2c + 6 = 5

2c = 5 - 6

2c = -1

c = -1 / 2 ----> ANSWER