(f(fx)) = 2x +4 when f(X) = 1... how do I solve this

not 100% clear on this one but I'll take a shot :)

I think you intended to write:
f(f(x))=2x+4
solve when f(x)=1
so I'd just substitue 1 for f(x)
f(1)=2x+4
which is simple then:
f(1)=2*1+4=2+4=6

hopefully someone else will agree or disagree with this result

I'll have to disagree. You made a mistake. You substituted 2x for 1, when fx=1.

I'm not going to try to defend my answer since I was never really confident in it to begin with. What would you suggest for an answer?

I think you're right asterisk.

Quote:

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Originally Posted by asterisk_man

not 100% clear on this one but i'll take a shot :)

i think you intended to write:
f(f(x))=2x+4
solve when f(x)=1
so i'd just substitue 1 for f(x)
f(1)=2x+4
which is simple then:
f(1)=2*1+4=2+4=6

hopefully someone else will agree or disagree with this result

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You substituted 1 for x, when really f(x) is 1. It's just a common mistake. Unless you did something I'm not aware of, then I would be the one who is incorrect.

He substituted f(x) as 1, the OP stated f(f(x)), so that would be f(1), so he's right there I believe

EDIT: on second thoughts I'm not so sure

No no no. Listen. On the right side of the simplified equation, where it said 2x+4 he substituted x for 1 so that the equation was 2*1+4, but x does not equal 1. F(x)=1

My thought process was as follows:
substitute 1 for f(x)
f(1)
then I just did what I would typically expect to do when I see f(something), substitute something for x.
again, I agree that this doesn't make me feel warm and fuzzy. I made some assumptions since I didn't see a better solution. No one has any thoughts on how else this might be solved? It seems like we can all agree that we get to f(1)=2x+4. but what's next? Maybe substituting f(x)=1 is the wrong thing to do. Ideas?

Ok, here's the way I see it. It said F(x)=1, or f*x=1, or fx=1. So if you were substituting for f(x) or fx, you would get 1, but you wouldn't get x=1; only fx=1. So by saying f(x)=f(1) you are incorrect.

Because it is taking so long for me to explain, I'll do it myself.

(f(fx)) = 2x +4 when f(X) = 1

if fx=1, f(fx)=f(1)

f=2x+4... f(1)=1*f=f

In terms of "f", f=2x+4
In terms of "x", x=-f/2+2

That's as much as I can get out of it.

But I have a question for the original asker. In what terms should the question be answered in?

you can't multiply around the f like that, f(x) means a function of x, it isn't a variable.

I agree that the OP probably typed it wrong :p

Ahhh. I see where our thoughts differ now.
You interpret f(x) as f*x but I interpret f(x) as the function f with input x.
I agree with your result if f(x) is intended to be f*x but f(x) is just so universally "a function 'f' with input 'x'" that I have a hard time imagining that it isn't.

I think we all agree that the OP needs to clarify but I think at this point we're the only ones who still care. :)

I couldn't agree more.