Question

设m>0,已知函数fx=2^x/m-m/2^x为奇函数

Answer 1

f(x)=-f(x) f(x)+f(-x)=0 f(0)=0

2^0/m-m/2^0=0

1/m-m=0

m=±1

m=1

f(x)=2^x-1/2^x

x1>x2

2^x1-1/2^x1-2^x2+1/2^x2

=(2^x1-2^x2)+(1/2^x2-1/2^x1)>0

f(x)增

m=-1

f(x)=-2^x+1/2^x

x1>x2

-2^x1+1/2^x1+2^x2-1/2^x2

=-(2^x1-2^x2)-(1/2^x2-1/2^x1)