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Let

f(x) = 12 - 2x if x <= 4

f(x) = ax + b if x > 4

 

The function f has the property that f(f(x)) = x for all x. What is a + b?

 Oct 21, 2021
 #1
avatar+115340 
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Let

f(x) = 12 - 2x if x <= 4

f(x) = ax + b if x > 4

 

The function f has the property that f(f(x)) = x for all x. What is a + b?

 

I started by drawing the g part I know:

 

I can see from this that if x<4 then  f(x)>4

 

f(0)=12-0=12

f(12)=12a+b=0

12a+b=0   (1)

 

f(1)=12-2=10

f(10)=10a+b=1

10a+b=1 (2)

 

Solve (1) and (2)  simultaneously and you get a=-0.5  and b=6

 

I checked this answer and it worked fine.

 Oct 21, 2021

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