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Let

 

f(x) = ax + 3 if x > 2

f(x) = x + 5 if -2 <= x <= 2

f(x) = 2x - b if x <= -2

 

Find a+b if the piecewise function is continuous

 Nov 4, 2021
 #1
avatar+9364 
+2

Let:

f1(x)  =  ax + 3

f2(x)  =  x + 5

f3(x)  =  2x - b

 

If the function is continuous, that means  f1(2)  must equal  f2(2)  and also that  f3(-2)  must equal  f2(-2)

 

f1(2)  =  f2(2)

a(2) + 3  =  2 + 5

2a + 3  =  7

2a  =  4

a  =  2

 

f3(-2)  =  f2(-2)

2(-2) - b  =  -2 + 5

-4 - b  =  3

-b  =  7

b  =  -7

 

And so

 

a + b  =  2 + -7  =  -5

 

Check: https://www.desmos.com/calculator/xdgxm9i5yb

 Nov 4, 2021
 #2
avatar+115335 
+1

Hi Hectictar,

It is really good to see you here  :)

 Nov 4, 2021

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