Find the values of a and b so that f(x) is continuous everywhere

Question

Question: Find the values of a and b so that f(x) is continuous everywhere 

- Just to be clear, f(x) is a piecewise function

 

f(x) = 3x-4, x > 4

          a + √x, 0 < x ≤ 4

          2x³-3b, x ≤ 0

Answer 1

f(x) is continuous at x = 4 if 3(4) - 4 = a + √4

 

                                                   8 = a + 2     a = 6

 

f(x) is continuous at x = 0 if 6 + √0 = 2(0)³ - 3b

 

                                                 -3b = 6

 

                                                    b = -2