Suppose f(x) = {a+bx, x<1,4,x=1,b-a,x, x>1} and if lim_x→1 f(x) = f(1), what are possible values of a and b?

lim_x→1^- f(x) = lim_x→1^- (a+bx) = a + b

lim_x→1⁺ f(x) = lim_x→1⁺ (b-ax) = b - a

f(1) = 4

Since lim_x→1 f(x) = f(1), we have

a + b = 4 and b - a = 4

Solving, a = 0 and b = 4

∴ possible values are a = 0, b = 4

Thus, the respective possible values of a and b are 0 and 4.