Here the step involves substituting 1-x for x in function equation.
Suppose f(x)=1-x
Now sub 1-x for x then f(1-x)=1-(1-x)=x
f(x)!=f(1-x)
Only D satisfy the condition.
f(x)=x^2(1-x)^2
f(1-x)=(1-x)^2(1-(1-x))^2(1-x)^2.X^2
f(x)=f(1-x)
Pick D
gmatprep - functions
This topic has expert replies
Source: Beat The GMAT — Problem Solving |
-
goyalsau
- Legendary Member
- Posts: 866
- Joined: Mon Aug 02, 2010 6:46 pm
- Location: Gwalior, India
- Thanked: 31 times
selango wrote:Here the step involves substituting 1-x for x in function equation.
Suppose f(x)=1-x
Now sub 1-x for x then f(1-x)=1-(1-x)=x
f(x)!=f(1-x)
Only D satisfy the condition.
f(x)=x^2(1-x)^2
f(1-x)=(1-x)^2(1-(1-x))^2(1-x)^2.X^2
f(x)=f(1-x)
Pick D
Can you please explain this step,
and is there any other way to solve these type of questions?
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Since the correct answer has to work for all values of x, we can plug in our own value for x.Gurpinder wrote:
Plug in x=2. Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1). The question becomes:
For which of the following functions does f(2) = f(-1)?
Answer choice A:
f(2) = 1-2 = -1.
f(-1) = 1-(-1) = 2.
Doesn't work.
Answer choice B:
f(2) = 1 - 2^2 = -3.
f(-1) = 1 - (-1)^2 = 0.
Doesn't work.
Answer choice C:
f(2) = 2^2 - (1-2)^2 = 4 - 1 = 3.
f(-1) = (-1)^2 - [1-(-1)]^2 = 1-4 = -3.
Doesn't work.
Answer choice D:
f(2) = 2^2 * (1-2)^2 = 4 * 1 = 4.
f(-1) = (-1)^2 * [1-(-1)]^2 = 1 * 4 = 4.
Success!
Answer choice E:
f(2) = 2/(1-2) = -2.
f(-1) = (-1)/[(1-(-1)] = -1/2.
Doesn't work.
The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
Gurpinder
- Legendary Member
- Posts: 659
- Joined: Mon Dec 14, 2009 8:12 am
- Thanked: 32 times
- Followed by:3 members
hey Mitch,
using your method, a question such as this one would be
lets say a=1 and b=2
so f(3) = f(1) + f(2)
So the question becomes for which of the following functions does f(1) + f(2) equal f(3)?
Is that right?
using your method, a question such as this one would be
lets say a=1 and b=2
so f(3) = f(1) + f(2)
So the question becomes for which of the following functions does f(1) + f(2) equal f(3)?
Is that right?
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
- Alfred A. Montapert, Philosopher.
-
GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Exactly right!Gurpinder wrote:hey Mitch,
using your method, a question such as this one would be
lets say a=1 and b=2
so f(3) = f(1) + f(2)
So the question becomes for which of the following functions does f(1) + f(2) equal f(3)?
Is that right?
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
-
Gurpinder
- Legendary Member
- Posts: 659
- Joined: Mon Dec 14, 2009 8:12 am
- Thanked: 32 times
- Followed by:3 members
Thank you!
For the first time in my life, I understand functions! =)
For the first time in my life, I understand functions! =)
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
- Alfred A. Montapert, Philosopher.
