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**Vedanti****Member**- Registered: 2017-12-19
- Posts: 5

I'm really stuck on this math problem...does anyone get it?

Given that f(3)=5 and f(3x)=f(x)+2 for all x, find the inverse of f(11).

Thanks in advance!

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**Alg Num Theory****Member**- Registered: 2017-11-24
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What is the domain of the function *f*? It certainly cannot include 0, otherwise

Vedanti wrote:

f(3x)=f(x)+2 for all x

would imply 0 = 2 upon substituting *x* = 0. Please state the question more fully.

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,400

hi Vedanti

Welcome to the forum.

When I meet a new puzzle I try to collect data so I get an idea what is happening.

We know that f(3) = 5 and that f(3x) = f(x) + 2, so my first try was

If f(9) = f(3 times 3) = f(3) + 2 = 5 + 2 = 7

and then

If f(27) = f(3 times 9) = f(9) + 2 = 7 + 2 = 9

So we know f(3) = 5, f(9) = 7 and f(27) = 9. The pattern is that when the input goes up by a power of three the value goes up by 2.

This suggested log (all in base 3)

Is that enough of a hint ?

Incidentally, log is not defined at 0.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**Vedanti****Member**- Registered: 2017-12-19
- Posts: 5

Thanks a lot! I get it now!

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