Find values for a and b so that f is a continuous function

Question

f(x)= ax-1, x<2

=3, x=2

=4-bx, x>2

Answer 1

For f to be continuous, we need all three parts to have the same value at x = 2. I.e.:

2a - 1 = 3

4 - 2b = 3

a = 2

b = 1/2