Question

下列命題中,真命題是(　　)

A．?m∈R,使函數(shù)f(x)=x2+mx(x∈R)是偶函數(shù)

B．?m∈R,使函數(shù)f(x)=x2+mx(x∈R)是奇函數(shù)

C．?m∈R,函數(shù)f(x)=x2+mx(x∈R)都是偶函數(shù)

D．?m∈R,函數(shù)f(x)=x2+mx(x∈R)都是奇函數(shù)

Answer 1

A

∵當(dāng)m=0時(shí),f(x)=x²(x∈R),∴f(x)是偶函數(shù).
又∵當(dāng)m=1時(shí),f(x)=x²+x(x∈R),
∴f(x)既不是奇函數(shù)也不是偶函數(shù).C、D錯(cuò).
當(dāng)x≠0,x∈R時(shí),f(-x)=x²-mx≠-(x²+mx)=-f(x),∴B不成立.故選A.