<p>it's in the blue book, test #7, section 9, number 16.
Q: Let (x) be defined as (x)= x^2-x for all values of x. If (a)= (a-2), what is the value of a? </p>
<p>Options: a) 1
b) .5
c)1.5
d) 6/5
e) 3</p>
<p>I'm very confused by this problem. Thanks.</p>
<p>Treat (x) as a new variable. You could call it f(x) if you want. So, (a) is just f(a). So, f(a) = f(a-2). What is f(a)? Well, f(a) is what you get when you plug a for x into f(x). So, f(a) = a^2 - a. Similarly, f(a-2) = (a-2)^2 - (a-2). </p>
<p>Thus, a^2 - a = (a-2)^2 - (a-2). </p>
<p>Foil: a^2 - a = a^2 - 4a + 4 - a +2 </p>
<p>Eliminate a^2 and -a from both sides: 0 = -4a + 6</p>
<p>Add 4a to both sides: 4a = 6. </p>
<p>Thus, a = 3/2 or 1.5 = C</p>
<p>oh, i realize what mistake i made. when foiling the -(a-2), i got the positives and negatives wrong. thanks for the help :)</p>
<p>yeah, i basically solved it like pontigier</p>