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/
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