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?
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.