Determine the constants is continuous at R

Question

Determine the constants a and b so that the function f(x) below is continuous at R

ax^2+b/x-2, x<2

2-3x, x≥2

Answer 1

When x = 2, 2 - 3x = -4

So, we want the limit of [(ax²+b)/(x-2)] as x approaches 2 from the left to equal -4

This will be true when a = -1 and b = 4 because (ax²+b) / (x-2) = (-x²+4)/ (x-2) = -(x²-4)/(x-2) = -(x+2)