Question

求函数f(x)=(x^3-x)/(x^2+1)^2的值域.急

Answer 1

该函数是奇函数.f(0)=0 x→+∞时f(x)→0

f'(x)=[(3x^2-1)(x^2+1)-(4x^4-4x^2)]/(x^2+1)

令f'(x)=0得：x^4-6^2+1=0

解得：x1^2=3+2√2 或x2^2=3-2√2

f(x1)=f[√(3+2√2)]=[√(6+4√2)]/2

︱f(x1)︱>︱f(x2)︱

考虑到函数的奇偶性.

∴函数的值域为：[-[√(6+4√2)]/2,[√(6+4√2)]/2]