f((f(f(x)) problem

[rongmon]

if f(x) = 1/(1-x),  then f(f(f(x)) equals

a. 1/(1-x)

b. x

c. 1/x

d. 1-x



thanks

[Noel]

B

[rongmon]

thanks..wonder why i am ending up with option a.

[Noel]

[Noel]

[rongmon]

thanks-a-ton!

[Ashima]

Yes it's B

[rongmon]

f (x) = (1-x)/(1+x), x not equal to -1

f (f (1/x)) is

a. 1
b. x
c. x^2
d. 1/x


Thanks
       

[Homer Simpson]

getting (d)

[rongmon]

right you are.

can you share the workings?

[Homer Simpson]

here it is - f(f(1/x)) = f(1-(1/x)/1+(1/x)) - substitute (1/x)
                           = f(x-1/x+1)
                           = [1 - (x-1)/(x+1)]/[1+ (x-1)/(x+1)] - substitute (x-1)/(x+1)
                           = (x+1 - x+1)/(x+1 + x-1)
                           = 1/x

[rongmon]

thanks!

[rongmon]

the second step,

you have (x-1) as numerator right, how is that reversed in the step below

[rongmon]

Figured, thanks.

[Homer Simpson]

ok :)