Question

【題目】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

【答案】A

【解析】∵當(dāng)m=0時,f(x)=x2(x∈R),∴f(x)是偶函數(shù).

又∵當(dāng)m=1時,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.

當(dāng)x≠0,x∈R時,f(-x)=x2-mx≠-(x2+mx)=-f(x),∴B不成立.故選A.