PSAT Math Question on Functions

Date: 10/17/2003 at 18:31:47
From: Kevin
Subject: PSAT math problem

I'm studying for PSAT's and I'm stuck on this question.  Can you help 
me?  For all values of r, let *r be defined as *r = (r + 2)/2.  If *4  
= x, then *x =

A 3/2
B 2
C 5/2
D 3
E 4

Date: 10/20/2003 at 11:18:10
From: Doctor Justin
Subject: Re: PSAT math problem

Hi Kevin,

This is a basic function problem that you will often run into when 
taking the SAT or PSAT, so it is good to know how functions work.

Let's start with what a function actually is and does.  A rough 
definition of a function is a correspondence between two sets.  This 
means that when you input a number, exactly one other number will be
the output.

An example of a function is as follows:

                           P(x) = 2x

If you were to input 5 into the function, your output would be 10:

                           P(5) = 2*5 = 10

In my example, you can think of P as the name of the function, x 
as the input, and 2x as the formula for the output.  Functions have 
many applications in mathematics, and the following item from our
archive provides a nice introduction to this notation:

  What Is a Function?

    http://mathforum.org/library/drmath/view/54545.html 

In your problem, * is the name of the funtion, r is the input, and 
(r + 2)/2 is the formula for the output.  To find x you must first 
input 4:

                            *4 = (4 + 2)/2 = 3

Thus, *4 = 3 and *4 = x so 3 = x.

We are trying to find *x, so substitute 3 into the function and you 
should find the desired output.

Does this help? 

- Doctor Justin, The Math Forum
  http://mathforum.org/dr.math/