Function

This topic has expert replies
Junior | Next Rank: 30 Posts
Posts: 23
Joined: Wed Mar 19, 2014 11:10 pm
Thanked: 1 times
Followed by:1 members

Function

by NaimaB » Sat Dec 06, 2014 9:07 am
Given that f(x) = x/{x+1}, for what value of k does f(f(k) = 2/3?

(A) -2

(B) 5/3

(C) 1

(D) 2

(E) 8

I did not understand the question. From where this k comes? I took this question from avengers group discussion.

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Sat Dec 06, 2014 10:54 am
Hi NaimaB,

This question can be solved algebraically or by TESTING THE ANSWERS. Before we get to the solution, here's some perspective on what all of this "means":

f(X) = X/(X+1) can be graphed (it's essentially just a "plug in" prompt). Plug in a value for X and you get a result.

For example:

f(0) = 0/(0+1) = 0/1 = 0
f(1) = 1/(1+1) = 1/2
f(2) = 2/(2+1) = 2/3
Etc.

This question comes with the added "quirk" that you have to use the function TWICE: f(f(K) = 2/3 means that you plug in a number, then plug in the RESULT of THAT calculation and you end up with 2/3.

I mentioned earlier that you can solve this problem with algebra or you can TEST THE ANSWERS. Since I've already done some math, I'll focus on that approach. From the above examples, you can see that....

f(2) = 2/3

2/3 is the result that we're looking for, but we need to use the function TWICE and here we've only used it once. So now we have to figure out how to get 2 as a RESULT:

X/(X+1) = 2

X = 2(X+1)
X = 2X + 2
-2 = X

So, f(f(-2) = 2/3

We can test this out by running through the calculations:

f(-2) = -2/(-2+1) = -2/-1 = 2

Now we plug in the "2":

f(2) = 2/(2+1) = 2/3

This is a match for what we're looking for!

Final Answer: A

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Tue Dec 09, 2014 8:29 am
I did not understand the question. From where this k comes?
This is something that a lot of students get confused about - the structure of function questions can be very tricky.

If the GMAT says:
If f(x) = 2x + 2, and f(m) = 8, what is the value of m?

Here's how to break down what this means:

f(x) means "the function that we perform on any given number x."

f(m) or f(k) or any other variable means "this function applied to the specific unknown number m (or k or whatever)."

So when they give you f(x), it's the general rule applied to any x. When they follow it up with f(any other variable), that variable is referring to a SPECIFIC number.

So here, f(f(k)) means "the function of the function of the specific number k." First, we'd figure out how to set up f(f(x)). We plug the whole function f(x) in as x:
Image

Then, we're told that that function of k is equal to 2/3. Plug in k and simplify:
Image

When we cross-multiply from there, we're left with:

3k = 2(2k + 1)
3k = 4k + 2
-k = 2
k = -2

The answer is A.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pm
Location: New Delhi, India
Thanked: 205 times
Followed by:24 members

by GMATinsight » Wed Dec 10, 2014 4:23 am
NaimaB wrote:Given that f(x) = x/{x+1}, for what value of k does f(f(k) = 2/3?

(A) -2

(B) 5/3

(C) 1

(D) 2

(E) 8

.
Another Observation which can make this question very easy is this

Given: f(x) = x/{x+1}

and also Given that

f(f(k)) = 2/3
i.e. f(f(k)) = f(k) / [f(k) +1] = 2/3 = 2/(2+1)
i.e. f(k) = 2
i.e. k/(k+1) = 2 = (-2)/(-2+1)

i.e k = -2

Answer: Option A
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour