# Thread: f(f(x)) problem

1. ## f(f(x)) problem

Can someone give me advice on this brain scrambler?

6x-8 is the output, but I must find f(x) in order to input f(f(x)) to create such an output.
Any ideas on how to tackle this problem?

2. ## Re: f(f(x)) problem

Originally Posted by bossbasslol
Can someone give me advice on this brain scrambler?

6x-8 is the output, but I must find f(x) in order to input f(f(x)) to create such an output.
Any ideas on how to tackle this problem?
I think this might be your interpretation of the problem. Can you state the problem exactly as it was stated to you?

3. ## Re: f(f(x)) problem

I would assume $\displaystyle f(x)$ is linear:

$\displaystyle f(x)=ax+b$

And then:

$\displaystyle f(f(x))=a(ax+b))+b=a^2x+(a+1)b=6x-8$

Equating coefficients, we then have:

$\displaystyle a^2=6$

$\displaystyle (a+1)b=-8$

Can you proceed?

4. ## Re: f(f(x)) problem

You have helped me a ton lately, and yes, this is the concept I was looking for. As long as I have the grasp of a and b, I can solve for them and continue on. Thank you for your kick starter.