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## #1 2017-12-19 13:11:37

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).

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## #2 2017-12-19 17:16:54

Alg Num Theory
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Registered: 2017-11-24
Posts: 27
Website

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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## #3 2017-12-19 21:38:33

bob bundy
Registered: 2010-06-20
Posts: 8,206

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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## #4 2017-12-20 03:15:05

Vedanti
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Registered: 2017-12-19
Posts: 5