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Question: If f(x) = \(\frac{1}{1 - x}\)then f(f(f(x))) is equal to...

If f(x) = 11−x\frac{1}{1 - x}then f(f(f(x))) is equal to

A

f(x), x ≠ 1

B

f(x), x ≠ 1, 0, -1

C

f(x), x ≠ 1, 0

D

f(x), x ≠ 1, -1

Answer

f(x), x ≠ 1, 0

Explanation

Solution

f(f(x)) = 11−11−x=x−1x\frac { 1 } { 1 - \frac { 1 } { 1 - x } } = \frac { x - 1 } { x } , x ≠ 0, 1

f(f(f(x))) = x−1x−1x−1x=11−x\frac { \frac { x - 1 } { x } - 1 } { \frac { x - 1 } { x } } = \frac { 1 } { 1 - x }= f(x), x ≠ 1, 0