Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

F(-2) = F(4) and F(4) = F(16) so F(-2) = F(16) and thus F(16) - F(-2) = 0.

Answer is B.

By the way, since you cannot make any assumptions about the nature of the function in this problem, D and E can be eliminated immediately. They are trap answers:

D) F(3) = 3 * F(3)
E) F(0) = 0

The 3 in D and 0 in E appear to come out of thin air; really what the test writer is hoping is that an unwary person inserts an assumption about the nature of the function. If you know nothing about the function then you cannot possibly have a definitive value (like 3 and 0) in the answer.

In general, there are two distinct parts of these type of function questions. The first is the domain, which are all the values for X in F(X). The second is the actual function itself. The plan of attack should depend on what information is given:

(1) The actual function itself is not given (as in this question) - you must work with the domain, which are the possible values of X.

(2) The function is given - you probably will need to work with both the domain and the function

For situation (1) where the function itself is not given, approach the problem like my explanation on this problem. Find possible values of X in the domain and use the information provided to manipulate F(x) where x is any value in the domain X.

Here's another problem discussed in these forums:

For which of the following functions f is f(x) = f(1-x) for all x?

Pick values of x and plug into both sides of the equation:
f(0) = f(1)
f(1) = f(0)
f(2) = f(-1)

For situation (2) where the function is given, first pick some domain value(s) that are "easy" to use, then plug those values into the function.

The same problem:

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)

From the discussion above we know f(0) = f(1) so the two values of x that we should be using are 0 and 1. We choose these because they are extremely easy values to plug in given functions in choices A-E;

A. f(0) = 1 - 0 = 1
f(1) = 1 - 1 = 0 ---> f(0) is not equal to f(1). Incorrect.

Sometimes two values x in the domain X can yield the same result for a given function. This is a property of functions - two values x in the domain X can have the same result. If this is the case, pick a new value of x (hopefully an "easy" value) and retest.

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)

From the discussion above we know f(0) = f(1) so the two values of x that we should be using are 0 and 1. We choose these because they are extremely easy values to plug in given functions in choices A-E;

A. f(0) = 1 - 0 = 1 f(1) = 1 - 1 = 0 ---> f(0) is not equal to f(1). Incorrect.

Sometimes two values x in the domain X can yield the same result for a given function. This is a property of functions - two values x in the domain X can have the same result. If this is the case, pick a new value of x (hopefully an "easy" value) and retest.

good approach. but here is one more. we need to calc f(1-x) as we are given f(x)

A ) f(1-x) = x not equal B) f (1-x) = 1 - (1-x) ^2 = 2x -x ^2 not equal C) f(1-x) = (1-x) ^ 2 - x ^2 = 1-2x not equal D) f(1-x) = (1-x)^2 (x)^2 equal.

Indian Application Disadvantage at Wharton’s MBA Program Recently I discovered an Indian application disadvantage at Wharton’s MBA program while reviewing their admissions data. I have been busy...

I opted to do my Team-Based Discussion (TBD) and interview in London with a member of the Admissions office. It was a benefit to have been through the...