Let f(x) be the function

Question

f(x)={x2−c for x<4,
{3x+4c for x≥4.

Find the value of c that makes the function continuous.

Answer 1

x^2-c and 3 x + 4 c
must be the same on both sides when x = 4

16 - c = 12 + 4 c

4 = 5 c

c = 4/5