For what value(s) of C is this function continuous at x=5?

Question

f(x)= x²-C, if x< 5

4x+2C, if x≥ 5

Answer 1

The function is continuous for C = 5/3.

For the piecewise function to be continuous, the left and right sides have to meet. That is to say, the top equation at x = 5 has to equal the bottom equation at x = 5.

So,

(5)^2 - C = 4(5) + 2C

25 - C = 20 + 2C

5 = 3C

C = 5/3

Hope that helped, Mycah!

Answer 2

If x = 5, f(x) = 4x + 2C (as defined)

f(x) is continuous for all values of C.