**P148. Show that there is no real constant c > 0 such that for all real numbers .**

**Solution:**

If the given equation holds for some constant c>0 then,

f(x) = for all

Putting x=0, we note

As

We put n=1 and x= to note that f(x) is not zero.

**Hence no c>0 allows f(x) =0 for all . (proved)**