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 500,000 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:
Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink]
14 May 2013, 19:47
Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+x|, x belongs to R a) 12 b)18 c)20 d)15
Answer: b) 18
Reason: We have to find the max. value of f(x). Max value of 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.
Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink]
30 May 2013, 13:21
With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, |3-x|...if we know that X>3 then we: -(3-x) = -3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0?
psychout wrote:
Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+x|, x belongs to R a) 12 b)18 c)20 d)15
Answer: b) 18
Reason: We have to find the max. value of f(x). Max value of 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.
Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink]
30 May 2013, 14:17
4
This post received KUDOS
WholeLottaLove wrote:
With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, |3-x|...if we know that X>3 then we: -(3-x) = -3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0?
x can be negative, negative numbers belong to R.
We can read the question as:
Find the maximum value of \(f(x) = 18-|3+x|\), x belongs to R Find the maximum value of \(f(x) = 18-(num\geq{0})\)
Remeber that an abs value is a number positive or equal to zero (never negative).
So what in which case the operation \(18-(num\geq{0})\) has the max-value? when the \(num\geq{0}\) is 0. Clearly \(18-0>18-1\) for example, so the max value is \(18\).
For the sake of clarity: This case corespond to x=-3, |3-3|=0. For any other value of x the quantity |3-x| will result in a positive value that you will subtract to 18, obtaining a lesser value (of course). _________________
It is beyond a doubt that all our knowledge that begins with experience.
Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink]
31 May 2013, 01:18
1
This post received KUDOS
Expert's post
WholeLottaLove wrote:
With numerous problems involving absolute value, we flip the signs inside the absolute value function if we know it to be a negative #. For example, |3-x|...if we know that X>3 then we: -(3-x) = -3+x. I'm guessing we don't do that here because in f(x) x cannot be less than 0?
psychout wrote:
Vamshiiitk wrote:
Find the maximum value of f(x) = 18-|3+x|, x belongs to R a) 12 b)18 c)20 d)15
Answer: b) 18
Reason: We have to find the max. value of f(x). Max value of 18-|3+x| will be 18 because the modulus will make |3+x|>=0. Lower the value of |3+x|, higher the value of 18-|3+x|=f(x). The lowest value of a modulus expression is 0, which implies f(x)=18-0=18.
Actually f(x) can be less than 0. For example, if x=20, then f(20)=18-|3+20|=-5 or if x=-25, then f(-25)=18-|3-25|=-4.
Now, the question asks about the maximum value of f(x)=18-|3+x| (f(x) is equal to 18 minus some non-negative value). To maximize f(x) we need to minimize |3+x|. The minimum value of |3+x| is 0, thus the maximum value of f(x)=18-|3+x|=18-0=0.
Hope it helps.
P.S. Notice that f(x) reaches its minimum for x=-3 --> f(-3)=18-|3-3|=18-0=0. _________________
Re: Find the maximum value of f(x) = 18-|3+x|, x belongs to R [#permalink]
24 Mar 2015, 23:51
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...