[tex]x \circ y=\frac{x y}{1-x-y+2 x y}[/tex]
a)
[tex]x \circ \frac{1}{2} =\frac{\frac{x}{2} }{1-x-\frac{1}{2} + x }=\frac{x}{2} \cdot 2=x[/tex]
b)
Lege comutativa:
x°y=y°x
[tex]\frac{x y}{1-x-y+2 x y}=\frac{yx}{1-y-x+2 yx}[/tex]
Se observa ca sunt egale
c)
[tex]f(x)\circ f(y)=\frac{\frac{x}{x+1}\cdot \frac{y}{y+1} }{1-\frac{x}{x+1}-\frac{y}{y+1}+2\frac{x}{x+1}\cdot \frac{y}{y+1}}[/tex]
[tex]f(x)\circ f(y)=\frac{xy}{(x+1)(y+1)-x(y+1)-y(x+1)+2xy} =\frac{xy}{xy+x+y+1-xy-x-xy-y+2xy} \\\\f(x)\circ f(y)=\frac{xy}{xy+1} =f(xy)[/tex]
Un alt exercitiu cu legi de compozitie gasesti aici: https://brainly.ro/tema/2520975
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