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Functions

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Source: — Quantitative Reasoning |
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by theCEO » Sun Jun 24, 2012 4:18 am
The easiest way is to substitute x with a number for example 2.

a
f(x) = 1-2 = -1
f(1-x) = 1--1=2

b
f(x) = 1-2^2= -3
f(1-x)= 1-(-1^2)= 0

c
f(x) = 2^2-(1-2)^2= 3
f(1-x) = -1^2-(1--1)^2= -3

d
f(x) = 2^2(1-2)^2 = 4
f(1-x) = -1^2(1--1)^2 = 4

e
f(x) = 2/1-2 = -2
f(1-x) = -1/1--1= -0.5

Answer is (d)
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by jcnasia » Sun Jun 24, 2012 5:37 am
Proof to show (d) is the correct answer:

f(x) = x^2 * (x - 1)^2
--> f(1-x) = (x - 1)^2 * ((1-x) - 1)^2
--> f(1-x) = (x - 1)^2 * (-x)^2
--> f(1-x) = (x - 1)^2 * x^2
--> f(1-x) = f(x)
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by Jim@StratusPrep » Sun Jul 08, 2012 3:45 pm
With the (x-1)^2 you need to look for an answer that eliminates the middle term when using the FOIL method

A) Adds a 1
B) Add the middle term
C) adds the middle term
D) Swaps middle term between two squares - CORRECT
E) Changes values in numerator and denominator.
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