1.
f(x)*(5x+1)=2x
5x*f(x)+f(x)=2x
(5f(x)-2)x=-f(x)
当f(x)≠2/5时有:
x=f(x)/(2-f(x))
所以f(x)的反函数为:f-1(x)=x/(2-5x)
2.
f-1(1/5)=(1/5)/(2-1)
f-1(1/5)=1/5
综上f-1(x)的值域为(f9(x)∈R,且x≠- 1/5)
1.
f(x)*(5x+1)=2x
5x*f(x)+f(x)=2x
(5f(x)-2)x=-f(x)
当f(x)≠2/5时有:
x=f(x)/(2-f(x))
所以f(x)的反函数为:f-1(x)=x/(2-5x)
2.
f-1(1/5)=(1/5)/(2-1)
f-1(1/5)=1/5
综上f-1(x)的值域为(f9(x)∈R,且x≠- 1/5)