Find the constants to make it continuous.

Question

I am having trouble starting this question. Find the constants (a, b or c) to make the function continuous.

f(x)= {

       x^-1  if x<-1
       ax+b  if -1 ≤ x ≤ 1/2
       x^-1  if x > 1/2

} I know that if you had only two function, you would set them equal to each other, plug in and solve for the variable, but here I don't know how I could do that.

Answer 1

Hint

You need to have continuity at the points where the function's definition is changing. So you need \begin{align*} f(-1) & = \lim_{x \to -1}f(x)\\ f(1/2) & = \lim_{x \to 1/2}f(x). \end{align*} Now solve for $a,b$.