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?

Guest Oct 21, 2021

#1**+2 **

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.

Melody Oct 21, 2021