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bmwhype2
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? Updated on: 25 Sep 2014, 23:28
Originally posted by bmwhype2 on 12 Nov 2007, 14:44.
Last edited by Bunuel on 25 Sep 2014, 23:28, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above

M19-14

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D
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 12 Nov 2007, 20:52
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after you have broken down to (1/1+x)

test a number, say x=2...

f(2)=2/3

f(1/2)=1/3

which is same as 1-f(x)...

D it is..
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 25 Sep 2014, 21:39
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\(f(x) = \frac{x}{x+1}\)

\(f(\frac{1}{x}) = \frac{\frac{1}{x}}{\frac{1}{x} + 1} = \frac{1}{x+1}\)

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

Answer = D
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 25 Sep 2014, 23:31
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If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above

M19-14
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\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} = \frac{1}{1 + x} = \frac{1 + x - x}{1 + x} = 1 - \frac{x}{1 + x} = 1 - f(x)\).

Answer: D.

Check other Functions questions in our Special Questions Directory.
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 10 Oct 2016, 15:31
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Plug in an value to test out the effect of (1/x) over (x) when fed into the function...

Say x = 3

f(3) = 3/(3+1) = 3/4
f(1/3) = (1/3)/[(1/3)+(3/3)] = 1/4

Thus f(1/x) = 1 - f(x)
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 10 Aug 2021, 20:53
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bmwhype2
If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above

M19-14

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

Answer: D.

Check other Functions questions in our Special Questions Directory.


VeritasKarishma can you pls explain the logic of solution above ...mostly get wrong answers when it comes to functions
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dave13

How do you find the expression of \(f(\frac{1}{x})\) ? Wherever you have x in f(x), put 1/x in its place.

\(f(\frac{1}{x})= \frac{\frac{1}{x}}{\frac{1}{x} + 1} \)

Now simplify it.

\(f(\frac{1}{x}) = \frac{1}{1 + x} \)

But \(f(x) = \frac{x}{x + 1}\)

Compare the two. \(f(\frac{1}{x})\) has 1 in numerator but f(x) has x. So add and subtract x in the numerator to get

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

If adding and subtracting x doesn't come to mind, use the options.
You see that f(1/x) is not the same as f(x) and neither as -f(x). Then try to simplify option (D) by putting in the value of f(x) in it and simplifying. Option (C) is trickier so try it at the end.

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... s-on-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... questions/
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 16 May 2024, 10:23
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Official Solution:

If \(f(x) = \frac{x}{x + 1}\), what is \(f(\frac{1}{x})\) in terms of \(f(x)\)?

A. \(f(x)\)
B. \(-f(x)\)
C. \(\frac{1}{f(x)}\)
D. \(1 - f(x)\)
E. none of the above


\(f(\frac{1}{x})= \frac{\frac{1}{x} }{\frac{1}{x} + 1} =\)

\(= \frac{\frac{1}{x} }{(\frac{1+x}{x})} =\)

\(=\frac{1}{x} *\frac{x}{x+1} =\)

\(=\frac{1}{1 + x} =\)

\(=\frac{(1 + x) - x}{1 + x} =\)

\(=\frac{1 + x}{1 + x}-\frac{x}{1+x}=\)

\(=1 - \frac{x}{1 + x} =\)

\(=1 - f(x)\)


Answer: D­
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If f(x) = x/(x + 1), what is f(1/x) in terms of x ? 10 Dec 2025, 01:44
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