Question

已知函数f(x)=(mx^2+2)/(3x+n)是奇函数,且f(2)=5/3 (1)求实数m和n的值;

Answer 1

∵f(x)=(mx^2+2)/(3x+n)是奇函数,且f(2)=5/3, ∴f(-x)=-f(x),即有

(mx^2+2)/(-3x+n)=-(mx^2+2)/(3x+n).

故有-3x+n=-(3x+n),从而得到n=0.

又f(2)=(4m+2)/6=5/3,∴m=2.

故f(x)=(2x^2+2)/3x=(2/3)(x+1/x).

设x10,x1x2>0(∵x1