# F(x)=f(2x)=3. Is it strictly a constant function?

1. Feb 12, 2012

### vkash

f(x)=f(2x)=3. Is it strictly a constant function??

1. The problem statement, all variables and given/known data

f(x)=f(2x)=3.
can we say that it is constant. Nothing else..

2. Relevant equations

BRAIN>>>>

3. The attempt at a solution

f(1)=f(1/2)=f(1/4)=f(1/8).........f(1/∞)=f(0)=3
I think no there can be many functions having such property and constant function is one of them.
AM i correct..?

2. Feb 12, 2012

### HallsofIvy

Re: f(x)=f(2x)=3. Is it strictly a constant function??

If you are saying that f(x)= 3 for all x, yes, that is a constant function. There are NOT "many functions" such that f(x)= 3 for all x!

3. Feb 14, 2012

### vkash

Re: f(x)=f(2x)=3. Is it strictly a constant function??

Is it possible for a function that it is not a constant function and obey the above written property?????

4. Feb 14, 2012

### Dickfore

Re: f(x)=f(2x)=3. Is it strictly a constant function??

no, for example, take f(x) =(-6)*cos(x), and x = 2pi/3. What do you get?

5. Feb 14, 2012

### Dickfore

Re: f(x)=f(2x)=3. Is it strictly a constant function??

oh, is it for all x? then, yes, provided that f is continuous around x=0.

6. Feb 14, 2012

### Dickfore

Re: f(x)=f(2x)=3. Is it strictly a constant function??

$$\left( \forall x \right) f(x) = f(2x) = 3 \Rightarrow \left( \forall x\right) f(x) = 3$$
This is by definition a constant function!

7. Feb 14, 2012

### blazeatron

Re: f(x)=f(2x)=3. Is it strictly a constant function??

To start , Forget about f(2x) for a while... f(x) = 3 implies that irrespective of what values the variable 'x' can take, the function value is 3 only... so , f(x) = 3 is a constant function for all values of x...The set of values takne by '2x' is actually a subset of values taken by 'x'...
This means that f(2x) is a subset of values taken by f(x).So , f(2x) is also a constant function like f(x).
The answer is : yes , the function is strictly constant