Find the value of a, b that makes the function continuous.

Question

f(x)=

 

4x^-1  for x<-1

 

ax+b  for -1≤x≤(1/2)

 

2x^-1 for x> (1/2)

Answer 1

You want ax + b = 4/x at x = -1

     a(-1) + b = 4/(-1)

     -a + b = -4

 

You also want ax + b = 2/x when x = 1/2

     a(1/2) + b = 2/(1/2)

     a/2 + b = 4

 

You have a system of two equations:

     -a + b = -4

     a/2 + b = 4

 

Solve by substitution or elimination.