More fun in 2015, part 16?

Calculus Level 5

Define a function f : R → R f : \mathbb R \to \mathbb R such that it satifies

f ( f ( x ) ) = f ( x ) 2015 f(f(x)) = f(x)^{2015}

Then how many polynomial functions satifies the above equation?

Bonus :- how many functions satifies the above relation? (don't input this as an answer)

2 1 4 0 Infinitely many 3

Krishna Sharma by Krishna Sharma , 24, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

we are asked to find number of polynomial functions.So let the degree of polynomial function be n.Then degree of f( f( x)) is n^2 and degree of ( f(x))^2015 is 2015n. therefore n^2=2015n.Hence f(x) is a constant polynomial or is a polynomial of degree 2015.There are three constant polynomials namely f(x)=o f(x)=1 and f(x)=-1 and a polynomial of degree 2015 which can be obtained by comparing the coefficients.Hence,there are in all 4 polynomial functions.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...