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If f(x)=1-(1/x), then f(f(f(x)))=?

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If f(x)=1-(1/x), then f(f(f(x)))=?

by Max@Math Revolution » Thu Dec 27, 2018 11:13 pm

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[Math Revolution GMAT math practice question]

If f(x)=1-(1/x), then f(f(f(x)))=?

A. x
B. 1/x
C. 1/x+1
D. -1/x+1
E. x/x+1
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answer

by Manasa3190 » Fri Dec 28, 2018 7:56 pm
f(x) = 1-(1/x)
f(x) = (x-1)/x

f(f(x)) implies substituting f(x) as x in above expression
f(f(x)) = (1-(1/x) -1 )/(1-(1/x))
f(f(x)) = -1/(x-1)

f(f(f(x))) = f(-1/(x-1))
Substituting 'x' as -1/(x-1) in f(x)
f(f(f(x))) = 1 - (1/(-1/(x-1)))
f(f(f(x))) = 1 + x -1
f(f(f(x))) = x
So, Option A is correct
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by Max@Math Revolution » Sun Dec 30, 2018 5:18 pm
=>

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

Therefore, the answer is A.
Answer: A
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by GMATGuruNY » Mon Dec 31, 2018 11:07 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If f(x)=1-(1/x), then f(f(f(x)))=?

A. x
B. 1/x
C. 1/x+1
D. -1/(x+1)
E. x/(x+1)
Let x=2 and apply the function three times:
f(2) = 1 - 1/2 = 1/2.
f(1/2) = 1 - 1/(1/2) = -1.
f(-1) = 1 - (1/-1) = 2.

The correct answer must yield a value of 2 when x=2.
Only A works.

The correct answer is A.
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