Question

函数f(X)=aX+b在R上满足f(x)=-f（-x）,且f（二分之一）＝二分之五.1.求实数a.b的值,2用定义证明f

Answer 1

f(-x)=-ax+b

f(x)=-f(-x)=ax-b=ax+b

故有b=0

f(x)=ax,f(1/2)=a/2=5/2,a=5

故有f(x)=5x

设-1