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If f(x) = 1 - 1/x, what is the value of f(f(f(x)))? 12 Dec 2022, 02:30
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A
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35% (medium)

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75% (02:01) correct 25% (02:01) wrong based on 136 sessions

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If \(f(x)=1-\frac{1}{x}\), what is the value of \(f(f(f(x)))\)?

A. \(x\)

B. \(\frac{1}{x}\)

C. \(\frac{1}{x+1}\)

D. \(\frac{-1}{x+1}\)

E. \(\frac{x}{x+1}\)


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A
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If f(x) = 1 - 1/x, what is the value of f(f(f(x)))? 12 Dec 2022, 02:42
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f(x)=1-1/x
f(x)= (x-1)/x

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

= -1/x-1

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

=x

option A correct
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If f(x) = 1 - 1/x, what is the value of f(f(f(x)))? 12 Dec 2022, 17:31
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See image for expression.

From there, add fractions and you'll end up with only \(x\).
Attachments

if fx 1-1dx.png
if fx 1-1dx.png [ 11.43 KiB | Viewed 2308 times ]

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If f(x) = 1 - 1/x, what is the value of f(f(f(x)))? 03 Dec 2024, 19:37
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\(f(x)=1-\frac{1}{x}\) and we need to find \(f(f(f(x)))\)

\(f(x)=1-\frac{1}{x}\) = \(\frac{x - 1}{x}\)
=> f(f(x)) = f(\(\frac{x - 1}{x}\))

Now, to find the value of f(\(\frac{x - 1}{x}\)) we need to replace x with \(\frac{x - 1}{x}\) in f(x) = \(\frac{x - 1}{x}\)

=> f(\(\frac{x - 1}{x}\)) = (((x-1)/x) - 1 ) / ((x-1)/x) = \(\frac{x - 1 - x }{ x - 1}\) = \(\frac{-1 }{ x - 1}\)
= \(\frac{1}{ 1 - x}\)

=> f(f(x)) = \(\frac{1}{ 1 - x}\)

=> f(f(f(x))) = f(\(\frac{1}{1 - x}\)) = ((1/(1-x)) - 1) / (1/(1-x))) = \(\frac{1 - (1-x)}{1}\) = 1 - 1 + x = x

So, Answer will be A
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

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If f(x) = 1 - 1/x, what is the value of f(f(f(x)))? 30 Jan 2026, 13:45
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