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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Help on PS problem- GMATprep ##### This topic has 2 expert replies and 3 member replies For which of the following functions f is f(x)=f(1-x) for all x? a. f(x)=1-x b. f(x)=1-x^2 c. f(x)=x^2-(1-x)^2 d. f(x)=x^2(1-x)^2 e. f(x)=x/(1-x) The answer is d. Need help in solving this. Legendary Member Joined 20 Dec 2006 Posted: 986 messages Followed by: 1 members Upvotes: 51 Prasanna wrote: For which of the following functions f is f(x)=f(1-x) for all x? a. f(x)=1-x b. f(x)=1-x^2 c. f(x)=x^2-(1-x)^2 d. f(x)=x^2(1-x)^2 e. f(x)=x/(1-x) The answer is d. Need help in solving this. Hi prassana .... when we say f(x)=f(1-x) ... it means that the eqn that represents f(x) should not change when x is replaced with (1-x) in that eqn .. and if u see it is only true for d ... for d it is given f(x) = x^2(1-x)^2 .. to find f(1-x) replace x with 1-x ... so we have f(1-x)= (1-x)^2(1-(1-x))^2 = (1-x)^2x^2 ... which is the same as f(x).. so D .... Master | Next Rank: 500 Posts Joined 26 Feb 2007 Posted: 418 messages Upvotes: 24 Gabriel Thanks for the answer. I had made a mistake in my calculations Prasanna Legendary Member Joined 27 Mar 2007 Posted: 559 messages Followed by: 2 members Upvotes: 5 For which of the following functions f is f(x)=f(1-x) for all x? a. f(x)=1-x b. f(x)=1-x^2 c. f(x)=x^2-(1-x)^2 d. f(x)=x^2(1-x)^2 e. f(x)=x/(1-x) a) f(x) = 1-x f(1-x) = 1-1+x = x Hence f(x) is not equal to f(1-x) b) f(x) = [1-x^2] f(1-x) = [1-(1-x)^2] = [1-(1+x^2-2)] =[2-x^2] Hence f(x) is not equal to f(1-x) c) f(x) = x^2-(1-x)^2 =x^2 - [ 1+x^2-2x] =x^2 - 1 - x^2 + 2x = 2x-1 f(1-x) = (1-x)^2 - [ 1 - (1-x)]^2 =(1+x^2-2x) - [x]^2 = 1 + x^2 - 2x - x^2 = 1-2x d)f(x)=x^2(1-x)^2 f(x) = x^2(1+x^2-2x) =x^2+x^4-2x^3 f(1-x) =x^2(1-x)^2 =[(1-x)^2] [ 1-(1-x)]^2 =[1+x^2-2x] [x^2] =x^2 + x^4 - 2x^3 Here f(x) = f(1-x) Hence D ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Prasanna wrote: For which of the following functions f is f(x)=f(1-x) for all x? a. f(x)=1-x b. f(x)=1-x^2 c. f(x)=x^2-(1-x)^2 d. f(x)=x^2(1-x)^2 e. f(x)=x/(1-x) Since we are not given any restrictions on the value of x, let’s let x = 1. Thus, we are determining for which of the following functions is f(1) = f(1-1), i.e., f(1) = f(0). Next, we can test each answer choice using our value x = 1. A. f(x) = 1 - x f(1) = 1 - 1 = 0 f(0) = 1 - 0 = 1 Since 0 does not equal 1, A is not correct. B. f(x) = 1 - x^2 f(1) = 1 - 1^2 = 1 - 1 = 0 f(0) = 1 - 0^2 = 1 - 0 = 1 Since 0 does not equal 1, B is not correct. C. f(x) = x^2 - (1 - x)^2 f(1) = 1^2 - (1 - 1)^2 = 1 - 0 = 1 f(0) = 0^2 - (1 - 0)^2 = 0 - 1 = -1 Since 1 does not equal -1, C is not correct. D. f(x) = x^2*(1 - x)^2 f(1) = 1^2*(1 - 1)^2 = 1(0)= 0 f(0) = 0^2*(1 - 0)^2 = 0(2) = 0 Since 0 equals 0, D is correct. Alternate Solution: Let’s test each answer choice using x and 1 - x. A. f(x) = 1 - x f(x) = 1 - x f(1 - x) = 1 - (1 - x) = x Since 1 - x does not equal x, A is not correct. B. f(x) = 1 - x^2 f(x) = 1 - x^2 f(1 - x) = 1 - (1 - x)^2 = 1 - (1 + x^2 -2x) = 2x - x^2 Since 1 - x^2 does not equal 2x - x^2, B is not correct. C. f(x) = x^2 - (1 - x)^2 f(x) = x^2 - (1 - x)^2 = x^2 - (1 + x^2 - 2x) = 2x - 1 f(1 - x) = (1 - x)^2 - (1 - (1 - x))^2 = 1 + x^2 - 2x - x^2 = 1 - 2x Since 2x - 1 does not equal 1 - 2x, C is not correct. D. f(x) = x^2*(1 - x)^2 f(x) = x^2*(1 - x)^2 f(1 - x) = (1 - x)^2*(1 - (1 - x))^2 = (1 - x)^2*x^2 Since x^2*(1 - x)^2 equals (1 - x)^2*x^2, D is correct. Answer: D ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13042 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 Prasanna wrote: For which of the following functions f is f(x)=f(1-x) for all x? a. f(x)=1-x b. f(x)=1-x^2 c. f(x)=x^2-(1-x)^2 d. f(x)=x^2(1-x)^2 e. f(x)=x/(1-x) The answer is d. Need help in solving this. Let's test the values using x = 0 So, we can reword the question as, For which of the following functions is f(0)=f(1-0) In other words, we're looking for a function such that f(0) = f(1) A) f(x)=1-x f(0)=1-0 = 1 f(1)=1-1 = 0 Since f(0) doesn't equal f(1), eliminate A B) f(x) = 1 - x² f(0) = 1 - 0² = 1 f(1) = 1 - 1² = 0 Since f(0) doesn't equal f(1), eliminate B C) f(x) = x² - (1-x)² f(0) = 0² - (1-0)² = -1 f(1) = 1² - (1-1)² = 1 Since f(0) doesn't equal f(1), eliminate C D) f(x) = x²(1-x)² f(0) = 0^2(1-0)^2 = 0 f(1) = 1^2(1-1)^2 = 0 Since f(0) equals f(1), keep D for now E) f(x) = x/(1-x) f(0) = 0/(1-0) = 0 f(1) = 1/(1-1) = undefined Since f(0) doesn't equal f(1), eliminate E Since only D satisfies the condition that f(x)=f(1-x) when x=0, the correct answer is D Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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