<p>Hey Latency, i just thought of another scenario for that stupid symmetry question…</p>
<p>What if f(x) = -x. Then f^-1(x) still equals f(x), and it’s symmetrical about the origin. You can no longer say it’s symmetrical across the line y=-x, because it is that line. </p>
<p>(Yes i know it’s symmetrical across y=x, but the only answer that satisfies both the scenarios — f(x) = -x & f(x) = x — is symmetric about the origin</p>
<p>Hmm, that’s a good point. I guess if something cannot be symmetric with itself, then the origin would be the right answer.</p>
<p>Interesting…did the question have “must” in it? Like, so and so MUST be symmetric across whatever. Not just "f(x) and f^-1(x) are symmetric about <this>. If it didn’t the question still sucks.</this></p>
<p>To Latency and 100Canadian, </p>
<p>Correct me if I’m wrong, but both of you seem to be working from the assumption that the function y=x is the only solution to f(x)=f^-1(x). Unless I’m missing something really obvious, wouldn’t f(x)=-x also fit this requirement, since y=-x is equivalent to -y=x? </p>
<p>One of Latency’s objections to using the origin as the point of symmetry for the function y=x was that this function is just as symmetrical about the line y=-x as it is about the origin. However, if we have to consider f(x)=-x as a solution to the requirement, then we would run into the same problem of saying a line is symmetric about itself if we choose y=-x as the line of symmetry.</p>
<p>Thus, we would run into this problem by saying the line of symmetry is either y=x or y=-x. I don’t know that saying a line is symmetric about itself is necessarily incorrect, but I think it makes more sense to avoid the problem altogether by saying that they’re both symmetrical about the origin. Answering the origin avoids the problem, and is correct for both f(x)=x and f(x)=-x. So while all three answers seem to have some truth to them, the origin seems to be the least questionable, unless I’m making some sort of dumb mistake in my math.</p>
<p>Another function which equals its inverse is f(x)=1/x, which is also symmetric about the origin (although it’s also symmetric about y=x and y=-x).</p>
<p>Wow I’m sorry, you two just made those posts while I was composing the exact same thing. Dang, I feel stupid for basically repeating what you two just said. Sorry 'bout that :)</p>
<p>Consider the equation f(x) = -x +5. The inverse of the function is identical to the function. It does not reflect over the origin. It does not reflect over y=-x. It does reflect over y=x. I’m pretty sure that it did have the word MUST in the problem. And also, y=x is symmetric about the line y=x. It’s the same line, but it’s still symmetric.</p>
<p>Wow. Winner. How did I not realize any linear function with the slope -1 is the inverse of itself. And here I was…trying to think of functions that are inverses of themselves when there is an infinite amount right there.</p>
<p>112358, that’s alright, you basically summed up what i was saying anyways, but in a better way haha.</p>
<p>Random747, that’s a good point… if this affects anything, you can still rotate that graph about the origin and end up with the inverse. But i’m not sure that counts as being “symmetrical” about the origin. But maybe it does, because it’s not <em>across</em> the origin, it’s <em>about</em> the origin?</p>
<p>I dont know. But i’m officially rattled.</p>
<p>And that question is a ***** :)</p>
<p>@100Canadian, I’m not sure what you mean by rotating the graph about the origin. That just doesn’t make any sense (given that we’re talking about the equation f(x)=-x+5). I don’t really think that the question is flawed, seeing that it does always work with y=x. And I don’t think the semantics of the question(about vs across) should serve to rule out y=x. Because if it can, then there would be no correct answer.</p>
<p>I think being symmetrical about the origin requires inversion across both the x and y axes, otherwise you could say that every function is symmetrical about the origin because any graph rotated 360 degrees will look the same as before.</p>
<p>I think y=x is the correct answer, although I really hope it’s not because aside from this question I already have 2 unanswered and 2 wrong, plus there are usually one or two that I miss without realizing it, so it’s looking like I may miss an 800 by just a couple questions.</p>
<p>Based on some of the traps people have fallen into, I’m thinking that it’s going to be 43+=800. Does that sound about right?</p>
<p>Just to clarify, here’s a link talking about inverse functions:
[Inverse</a> Functions](<a href=“http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html]Inverse”>http://www.uncwil.edu/courses/mat111hb/functions/inverse/inverse.html)
If you scroll down to “graphs” of inverse functions, it states that
“The graph of f^-1 is the reflection about the line y = x of the graph of f.”
If f^-1 and f are equal, it must be symmetrical to the line y = x.</p>
<p>Oh, and about the curve, it’s almost always either 44+ or 43+ as an 800, and I’m leaning towards 43+ because it seems to be a bit harder than usual.</p>
<p>what was the answer to the question about the palm tree?
for some reason I remember being unsure if I did it correctly…
I also put y=x but after reading discussion, I’m unsure what the answer really is…
does anyone else remember other questions/answers? I don’t think I did very well because I omitted 6. But I want to know if I got any other of the 44 that I answered wrong.</p>
<p>Thanks!</p>
<p>@infinity101 I remember a lot of the questions but probably shouldn’t put them up (will just lead to more worried people). For the palm tree, I’m not completely sure about this but i think it was tan(20) = x/100 so x=tan(20) *100, which is ~36. Then since the guy was 6 feet tall you add 6 so it’s 42. Correct me if I’m wrong on any of those values, because I don’t remember what answer I actually got.</p>
<p>was that choice “A”?</p>
<p>Alright well since I’m bored I’ll put up some questions. </p>
<p>For something about boys and girls I remember after 10 girls left there were twice as many boys . i think i got b =2(g-10)</p>
<p>For the one about in what ways could you solve an equation by graphing, i got I and III</p>
<p>For the one with 0<a<b i got II and III to both work</p>
<p>For the one with the standard deviation i got 8,10,10,10,10,12</p>
<p>For the one with the greatest integer less than or equal to x i got -1</p>
<p>For the recursive sequences one i got n^2 + 2 and whatever sequence matched up with that</p>
<p>For the one with the ln x = e^(-x) i got .27 ish?</p>
<p>I got .5 for the probability one </p>
<p>I got 10 for the number of lines on that number line</p>
<p>I remember getting .866 as an answer to something</p>
<p>I got -16 for the one with (k,6) and f(x) = logbase2(some equation i don’t remember)</p>
<p>i got the point (8,12) for the one where BC was twice as long as AB</p>
<p>i got 6 for the (2x,2y) one</p>
<p>I remember something about a trig one where it had sin^2 + cos^2 at the top over sin and then once you simplified it just required one operation to get the answer</p>
<p>I don’t remember the numbers but I think for one of them it was just degrees to radians</p>
<p>For the solid cone I got ~18</p>
<p>I got g(x) - h(x) is greater than or equal to 0 for that one where there were two functions and g(x) was above h(x).</p>
<p>I remember something about a triangle where the angle came out to be 120 degrees after using law of cosines</p>
<p>I don’t remember the question, but it was about the equation of a circle. I think I put E.</p>
<p>One of them had to do with a transformation, but I don’t remember what it was.</p>
<p>I’ll try to remember more and if I do I’ll post them. Btw, I hope this doesn’t cause more panic.</p>
<p>Oh and also, I read the sticky by the admin. Is this violating the rules?</p>
<p>But Zamxxx, as mentioned before, what if f(x) = x? It’s inverse equals the original f(x), but can you say the graphs are symmetrical to the line y=x if they actually are that line? I personally don’t think you can say that… but i’m beginning to think y=x is probably the answer (even though it’s technically wrong).</p>
<p>I don’t think there is an answer to that question, and i think we should complain about it to collegeboard to be honest…</p>
<p>@100Canadian, the rule to tell if something is symmetrical about y=x is that if you have a point (x,y), then you should have the point (y,x) on the inverse. If we had the point (2,2), then on the inverse we would have (2,2); it is symmetric. y=x is definitely the answer to that one imo.</p>
<p>K but i still don’t think you can say a line is symmetrical across itself.</p>
<p>What you said is true, but it makes more sense when f(x) does not equal its inverse. If f(x) does equal its inverse, as it said in the question, you can’t say f(x) is symmetrical across itself. At least, I don’t think you can.</p>
<p>But who knows how collegeboard people think… ;)</p>
<p>For the palm tree question, I believe I got a number around 54.</p>
<p>Damn random747, you’ve got some memory there.</p>