Given that the function f:R→R is defined by f(x)=x^n .For what values of n,if any,is fof=f.f? For each of these values of n find fof.


Question and Answers Forum

All Questions Topic List
Algebra Questions
Previous in All Question Next in All Question
Previous in Algebra Next in Algebra
Question Number 24764 by NECx last updated on 25/Nov/17

$G i v e n t h a t t h e f u n c t i o n f : R \to R$ $i s d e f i n e d b y f (x) = x^{n} . F o r w h a t$ $v a l u e s o f n, i f a n y, i s f o f = f . f ?$ $F o r e a c h o f t h e s e v a l u e s o f n f i n d$ $f o f .$
	Answered by mrW1 last updated on 25/Nov/17

	${(x^{n})}^{n} = x^{n} \times x^{n}$ $x^{n \times n} = x^{n + n}$ $\Rightarrow n \times n = n + n$ $\Rightarrow n = 0 o r 2$ $w i t h n = 0$ $f (x) = 1$ $f o f = 1$ $w i t h n = 2$ $f (x) = x^{2}$ $f o f = x^{4}$
	Answered by ajfour last updated on 25/Nov/17

	$f o f = f [f (x)] = f (x^{n}) = {(x^{n})}^{n} = x^{(n^{2})}$ $f . f = {(x^{n})}^{2} = x^{2 n}$ $f o f = f . f \Rightarrow n^{2} = 2 n$ $o r n (n - 2) = 0 \Rightarrow n = 0, 2$ $f o r n = 0 :$ $f (x) = x^{0} = 1 h e n c e f o f = 1$ $f o r n = 2 :$ $f (x) = x^{2} h e n c e f o f = x^{4} .$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum