Question

f(xy)=f(x)
and f(1) =3 then f(x) = ?

Answer 1

put x = 1 in f(xy) = f(x)
you will get f(y)

Answer 2

will f(x) be 3? i.e a constant?

Answer 3

yes

Answer 4

hmm..fir kuch galat kia maine :/

Answer 5

leme post whole q

Answer 6

so this is not the original question?

Answer 7

\[\LARGE \int\limits_1^{xy}f(t)dt=y \int\limits_1^{x}f(t)dt+x \int\limits_1^yf(t)dt\]
for all x and y and y=R+,f(1)=3 then
Options:
f(x)=3log(3x)
f(x)=log (base e)ex
f'(y)=3/4
f'(x)=1/x

Answer 8

\[\LARGE f(xy)(y+xy')=yf(x)+xf(y).y'\]
y'=0
\[\LARGE yf(xy)=yf(x)\]
\[\LARGE f(xy)=f(x)\]
is it correct?

Answer 9

@hartnn

Answer 10

just tossing it around a little ....
\[ \int_1^{xy}f(t)dt=y \int_1^{x}f(t)dt+x \int_1^yf(t)dt\]
\[ F(xy)-F(1)=yF(x)-yF(1)+xF(y)-xF(1)\]
\[ F(xy)-yF(x)-xF(y)=F(1)(1-y-x)\]
\[ f(xy)(x'y+xy')-y'F(x)-yf(x)x'-x'F(y)-xf(y)y'=F(1)(1-y'-x')\]

Answer 11

if this is wrt.x, then x'=1

\[f(xy)(y+xy')-y'F(x)-yf(x)-x'F(y)-xf(y)y'=-F(1)y'\]

yeah, i cant see anyting from this this early :/

Answer 12

Take the mixed partial with respect to x and y...simplify...you will get a simple equation in which you can solve for f

Answer 13

what is wrong with my solution?