# Function Question

1. Feb 19, 2017

### Arman777

1. The problem statement, all variables and given/known data
$f(xy)=f(x)+f(y)$ and $f(16)=16$, $f(2)=?$

2. Relevant equations
function properities

3. The attempt at a solution
$f(x)=y$ so
$f(xf(x))=f(x)+f(f(x))$
then I put
$xf(x)=16$
and
$f(x)+f(f(x))=16$
but this not much make sense,
I am really stucked

2. Feb 19, 2017

### PeroK

What about $f(4)$?

3. Feb 19, 2017

### Arman777

I dont know,where should I put it ?

4. Feb 19, 2017

### PeroK

5. Feb 19, 2017

### Arman777

I am thinking,I didnt understand where it will lead. $f(4f(4))=f(4)+f(f(4))$ so ?

6. Feb 19, 2017

### PeroK

Why are you taking $f(f(x))$?

7. Feb 19, 2017

### Arman777

whats that mean ?

8. Feb 19, 2017

### pasmith

f(16) = f(2*8) = f(2) + f(8) ...

9. Feb 19, 2017

### Arman777

I found that but ıts not going further.And from $xf(x)=16$ and from $f(x)+f(f(x))=16$ you said , $f(x)+f(16/x)=16$
so $f(4)=8$ and $f(2)+f(8)=16$ but we cant find $f(8)$ and also,I think we cant do these steps cause, we said $f(4)=8$ but we know that
$xf(x)=16$ so $4f(4)=32≠16$.

simply $f(x)+f(16/x)=16$ this is only true for an special $x$ not all $"x"$ s

10. Feb 19, 2017

### SammyS

Staff Emeritus
You should NOT be assuming that $\ y = f(x)\$ in the above statement.

The author of this question might just as well have stated this as follows:
$f(ab)=f(a)+f(b)$​

Aa examples,consider the following:
$f(35)=f(5)+f(7)$

$f(9)=f(3)+f(3)$
$=2f(3)$​

11. Feb 19, 2017

### Arman777

$f(16)=f(2)+f(8)=16$
$f(8)=f(4)+f(2)$
and $f(4)=8$ so,
$f(8)-f(2)=8$
$f(8)+f(2)=16$
$f(2)=4$

12. Feb 19, 2017

### Arman777

Still awkard..there must a solution which we can assume $y=f(x)$ and then solve it

13. Feb 19, 2017

### SammyS

Staff Emeritus
You should not assume that for the statement of this problem.

14. Feb 19, 2017

### Arman777

Ok,thanks..I am trying to solve this for like hours by using $y=f(x)$ ,which I was wrong

15. Feb 19, 2017

### PeroK

It's difficult to help any more without giving it away. Anyway, here's a bit hint: $4 \times 4 = 16$.

16. Feb 19, 2017

### Arman777

Thanks

17. Feb 19, 2017

### PeroK

$f(4 \times 4) = f(16)$

18. Feb 19, 2017

### Arman777

oh I see yeah..Thanks again

19. Feb 19, 2017

### SammyS

Staff Emeritus
I think @PeroK was trying to get you to answer his previous question: "What is ƒ(4) ?"

20. Feb 19, 2017

### Arman777

İts 8 I found it ?