GMAT PREP software question

[Kayode]

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

[Brent@GMATPrepNow]

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

f(x)= x²
f(x)= x+1
f(x)= √x
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)=x², does f(2) = f(1) + f(1)?
Plug in to get: 2² = 1² + 1²? (No, doesn't work)
So, it is not the case that f(2) = f(1) + f(1), when f(x)=x²

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

[CoachErf]

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.

[[email protected]]

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

[digvijayk]

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

[Aman verma]

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.