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Source: — Problem Solving |
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by theCEO » Sun Oct 25, 2015 4:33 pm
rommysingh wrote:if the function F is defined by F(x)=x^2+1/x^2 for all nonzero numbers X, then F(-1/X)=
A. -1/f(x)
B. 1/f(x)
C. 1-f(x)
D. -f(x)
E. f(x)
One way to solve is to pick a number. In this case pick the number 2

F(x)=x^2 + 1/x^2
F(2)=2^2 + 1/2^2 = 4 + 1/4 = 4.25

F(-1/x) = (-1/x)^2 + 1/(-1/x)^2
F(-1/2) = (-1/2)^2 + 1/(-1/2)^2 = 1/4 + 4 = 4.25

Thefore F(x) = F(-1/x)

ans = e
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by Matt@VeritasPrep » Sun Oct 25, 2015 10:01 pm
An even easier way is just use the function.

Since f(x) = x² + (1/x²) for ANY value of x, we can use (-1/x) as our value. Hence we just REPLACE x with -1/x, as shown:

f(x) = x² + (1/x²), so

f(-1/x) = (-1/x)² + 1/(-1/x)²

or

f(-1/x) = 1/x² + (1/(1/x²)), which is just (1/x²) + x², the same thing we had for f(x).

Thus f(x) = f(-1/x), since they output the same result.
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by Brent@GMATPrepNow » Mon Oct 26, 2015 6:45 am
Matt and theCEO have demonstrated the two methods (Algebraic and Input-Output) for solving a question type I call Variables in the Answer Choices.
If you'd like more information on these approaches, we have some free videos:
- Variables in the Answer Choices - https://www.gmatprepnow.com/module/gmat- ... /video/933
- Tips for the Algebraic Approach - https://www.gmatprepnow.com/module/gmat- ... /video/934
- Tips for the Input-Output Approach - https://www.gmatprepnow.com/module/gmat- ... /video/935

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Oct 29, 2015 1:22 am
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

if the function F is defined by F(x)=x^2+1/x^2 for all nonzero numbers X, then F(-1/X)=
A. -1/f(x)
B. 1/f(x)
C. 1-f(x)
D. -f(x)
E. f(x)




Consider (-1/x)^2= 1/x^2 and (1/(-1/x)^2)=x^2. So F(-1/x )=1/x^2 + x^2 = F(x).
So the answer is (E).
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