Game of function

Algebra Level 2

A non-constant function f(x) is such that f(2x)= $[f(x)]^2$ .

Find the value of x if f(x)=1.

This is an original problem and belongs to my set Raju bhai's creations

3 2 0 4

2 solutions

Skanda Prasad
Oct 31, 2017

Given $f(2x)=(f(x))^2$

And $f(x)=1$

Substituting in the first equation, we get,

$f(2x)=1^2$

$\implies$ $f(2x)=1$

$\implies$ $f(2x)=f(x)$

$\implies$ $x=2x$

$\implies$ $x(2-1)=0$

$\implies$ $\boxed{x=0}$

Rajath Rao
Oct 31, 2017

$\implies$ f(x)= $m^x$

Where m is any constant

Given that , f(x)=1

$\implies$ $m^x$ =1

Therefore, $\boxed{x=0}$