Find the values of a and b that make f continuous everywhere.

Algebra
Tutor: None Selected Time limit: 1 Day

(x^2 - 4) / (x-2)  if x< 2

f(x)=   ax^2 - bx + 3  if 2 </=  x < 3

4x - a + b   if  x =/>  3 

May 6th, 2015

we need to let f(x) continuous at x = 2 and x = 3

x = 2- 

f(x) = (x^2-4)/(x-2) = x+2 = 4

x=2+ 

f(x) = 4a-2b+3 = 4

 at 3- 

f(x) = 9a-3b+3 

at 3+ 

f(x) = 12-a+b =9a-3b+3

so 

4a-2b=1

10a-4b=9

a = 7/2 

b = 13/2 

May 6th, 2015

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