Question

If f(x)=1+x/1-x, prove that f(x)×f(x)^2/1+[f(x)]^2=1/2.​

Answer 1

Step-by-step explanation:

f(x)=

x−1

x+1

fof(x)=

f(x)−1

f(x)+1

=

x−1

x+1

−1

x−1

x+1

+1

=

x+1−x+1

x+1+x−1

=x

i)(fofof)(x)=f(fof(x))=f(x)=

x−1

x+1

ii)(fofofof)(x)=fof(fof(x))=fof(x)=x