GMAT PREP software question

Expert replies

Kayode: Newbie | Next Rank: 10 Posts; Posts: 5; Joined: Wed Apr 29, 2015 2:59 am

by Kayode » Tue May 05, 2015 8:04 am

I want to know how "function" work?

For example

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers?

a)f(x)=x^2

b)f(x)=x+1

c)f(x)=sqr root x

d)f(x)=2/x

e)f(x)=-3x

Like this post

Source: Beat The GMAT — Problem Solving | Tue May 05, 2015 8:04 am

GMAT/MBA Expert

Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue May 05, 2015 8:12 am

For which of the following functions f(a+b) = f(a) + f(b) for all positive numbers a and b?

f(x)= xÂ²
f(x)= x+1
f(x)= âˆšx
f(x)= 2/x
f(x)= -3x

One approach is to plug in numbers. Let's let a = 1 and b = 1

So, the question becomes, "Which of the following functions are such that f(1+1) = f(1) + f(1)?"
In other words, for which function does f(2) = f(1) + f(1)?

A) If f(x)=xÂ², does f(2) = f(1) + f(1)?
Plug in to get: 2Â² = 1Â² + 1Â²? (No, doesn't work)
So, it is not the case that f(2) = f(1) + f(1), when f(x)=xÂ²

B) If f(x)=x+1, does f(2) = f(1) + f(1)?
Plug in to get: 2+1 = 1+1 + 1+1? (No, doesn't work)
So, it is not the case that f(2) = f(1) + f(1)
.
.
.
A, B, C and D do not work.
So, at this point, we can conclude that E must be the correct answer.
Let's check E anyway (for "fun")

E) If f(x)=-3x, does f(2) = f(1) + f(1)?
Plugging in 2 and 1 we get: (-3)(2) = (-3)(1) + (-3)(1)
Yes, it works

The correct answer is E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

Like this post

CoachErf: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Mon May 04, 2015 10:13 amFollowed by: 1 member; Location: New York, NY; GMAT Score:770

by CoachErf » Tue May 05, 2015 8:41 am

Brent's approach is a good one.

Alternatively, you can think of this question a bit more conceptually. You're looking for the function for which the following condition applies:

An input of a +b will yield the same output as would the sum of the outputs when you input a and b individually

In other words, the correct answer should be a distributive function. Of the choices, the only function that has a distributive property is choice E.

Like this post

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

by [email protected] » Wed May 06, 2015 9:27 am

Hi Kayode,

"Functions" are essentially just another way to write out the formula for a graph.

For example....

Y = 2X + 1

can be written as....

f(X) = 2X + 1

Since you can physically graph a line by choosing values for X, then calculating the corresponding value for Y (and then graphing the co-ordinate), you can do the same thing with a function. This approach is usually the easiest way to deal with a function question on Test Day.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

Like this post

digvijayk: Master | Next Rank: 500 Posts; Posts: 113; Joined: Sun Sep 11, 2011 11:24 amFollowed by: 5 members; Location: GMAT Strategy Kingdom; Thanked: 43 times; GMAT Score:720

by digvijayk » Wed May 06, 2015 10:50 am

Simple example, say you put bananas(a) and milk(b) into a mixer(f). You run the mixer for a minute and you get an output= banana shake

So, function is something that takes in variables, works on them (just like the mixer) and yields results (banana shake).

On the GMAT, plugging in values will work.

If you're more interested, check out: https://www.khanacademy.org/math/algebr ... a-function

Follow my blog at: https://gmat0.blocked/

No business could ever survive without strategy, so how can your test preparation? Get your strategy in place today. Go to:

https://www.amazon.com/GMAT-Improve-Dras ... 00A7CTV1A/

Like this post

Aman verma: Master | Next Rank: 500 Posts; Posts: 304; Joined: Wed Jan 27, 2010 8:35 amFollowed by: 3 members; Location: International Space Station; Thanked: 11 times

by Aman verma » Thu May 07, 2015 2:58 am

Kayode wrote:I want to know how "function" work?

For example

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers?

a)f(x)=x^2

b)f(x)=x+1

c)f(x)=sqr root x

d)f(x)=2/x

e)f(x)=-3x

Hello Kayode,

Since, you want to know how functions work, here is an algebraic approach for this Functional Equation:-

Substitute the value of function given in each option into the original equation:

a)f(x)=x^2, f(a+b)=f(a)+f(b), (a+b)^2=(a^2)+(b^2),Invalid.
b)f(x)=x+1, f(a+b)=f(a)+f(b), (a+b+1)=(a+1)+(b+1),Invalid.
c)f(x)=x^1/2,f(a+b)=f(a)+f(b), (a+b)^1/2=(a^1/2)+(b^1/2), Invalid.
d)f(x)=2/x, f(a+b)=f(a)+f(b), 2/(a+b)=(2/a)+(2/b), Invalid.
e)f(x)=-3x, f(a+b)=f(a)+f(b), -3(a+b)=(-3a)+(-3b), Valid.

Hence E.

800. Arjun's-Bird-Eye

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review