Question

下列命題中是假命題的是(　　)

A．?α,β∈R,使sin(α+β)=sinα+sinβ

B．?∈R,函數(shù)f(x)=sin(2x+)都不是偶函數(shù)

C．?m∈R,使f(x)=(m-1)·是冪函數(shù),且在(0,+∞)上單調(diào)遞減

D．?a>0,函數(shù)f(x)=ln2x+lnx-a有零點(diǎn)

Answer 1

B

對(duì)于A,β=0時(shí),命題成立,故A為真命題;
對(duì)于B,當(dāng)=時(shí),f(x)=cos2x是偶函數(shù),∴B為假命題;
對(duì)于C,若f(x)為冪函數(shù),則m-1=1,∴m=2,此時(shí)f(x)=x^-1在(0,+∞)上單調(diào)遞減,故C為真命題;
對(duì)于D,f(x)=(lnx+)²--a,顯然?a>0,f(x)=0有解,故D為真命題.故選B.