Răspuns:
Explicație pas cu pas:
a)f(x)=(x²+1)/x Aratati ca f(x)=f(1/x)
f(1/x)=(1/x²+1)/1/x=(1+x²)/x² ·x=(x²+1)/x=f(x)
b)cum coordonatele sunt egale⇒x=f(x) ⇔2008x+2007=x⇔2007x= -2007⇔x=-1
f(-1)=-2008+2007=-1
astfel se obtine A (-1,-1) CE SATISFACE CONDITIA DIN ENUNT
c) f(x)-f(y)/x-y= (x²-y²)/x-y =(x-y)·(x+y)/x-y=x+y≥0(strict) (x,y≥0(strict)) x≠y
d)(f(a)-f(b))/a-b=(a√2+√2008-b√2-√2008)/a-b=√2(a-b)/a-b=√2∈R/Q,a≠b
e)(f(x)-f(y))/x-y=((x+1)/x -(y+1)/y) / x-y=((xy+y-xy-x)/xy)· 1/(x-y)= -1/xy≤0(strict)
(deoarece x,y ≥0(strict) ;xy≥0,1/xy≥0 -1/xy≤0)
