Wiskunde Multiple Choice Vraag

Als $f(x)=1+\frac1x$ dan is f( f(x) ) gelijk aan	A. $\left(1+\frac1x\right)^2$
	B. $2+\frac1x$
	C. $1+\frac2x$
	D. $1+\frac1{x^2}$
	E. $\frac{2x+1}{x+1}$

[ v8853 - op net sinds 26.3.2024-(E)- ]

Translation in E N G L I S H

IN CONS IN CONSTR IN CONSTRUC IN CONSTRUCTI IN CONSTRUCTION	A.
	B.
	C.
	D.
	E.

Oplossing - Solution

$\\f(f(x))=f\left(\!1+\frac1x\right)=1\!+\!\frac{1}{1+\frac1x}=1+\frac{1}{\frac{x+1}{x}}=1+\frac{x}{x\!+\!1}=\frac{x\!+\!1\!+\!x}{x+1}=\frac{2x+1}{x+1}$