Math Is Fun Forum

Vedanti

Member

Registered: 2017-12-19

Posts: 7

Please Help!

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!

Alg Num Theory

Member

Registered: 2017-11-24

Posts: 693

Website

Re: Please Help!

What is the domain of the function f? It certainly cannot include 0, otherwise

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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Me, or the ugly man, whatever (3,3,6)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,158

Re: Please Help!

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

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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
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Vedanti

Member

Registered: 2017-12-19

Posts: 7

Re: Please Help!

Thanks a lot! I get it now!