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)

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

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.

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

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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