Function

Algebra Level 1

Let f ( x ) = x + 1 x − 1 f(x) = \frac {x+1}{x-1} . Then f ( f ( 2010 ) ) f( f( 2010 ) ) equals?


The answer is 2010.

Trishit Chandra by Trishit Chandra , 23, India

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2 solutions

Trishit Chandra
Mar 4, 2015

12 Helpful 0 Interesting 0 Brilliant 0 Confused
Gamal Sultan
Mar 14, 2015

Since

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

Then

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

Then

f(f(x)) = x

Then

f(f(2010)) = 2010

Another solution

f(f(x)) ={ [(x + 1)/(x - 1)] + 1}/{[(x+ 1)/(x- 1)] - 1} = x

Then

f(f(2010)) = 2010

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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