September 5th, 2011, 02:26 PM  #1 
Senior Member Joined: Jun 2011 Posts: 154 Thanks: 0  Precalculus
Hello Everyone. Among plenty more problems in my precalculus class that I am having trouble with, this is one that has me the most baffled. If someone could please solve it and tell me how they did so I would be extremely grateful. Here it is: f(x) = 2x³5x ; g(x) = 2x/x5 (two x over x minus 5) All I am asked is to find fg I have been trying to solve this for a good while, and honestly, I am not sure if it is asking me to multiply the two functions, or to find f(g). Either way, I tried doing both and got no answer that was anywhere near the 5 choices given by my instructor, which are listed below. (note, 2x^5 means 2x to the 5th power etc.. If someone knows the ASCII code for "superscripts 4 and 5", please share them with me). 1. 2x^5+25x³75x 2. 2x^525x³75x 3. 2x^5+16x^4+25x³40x²75x 4. 2x^5+16x^435x³40x²75x 5. 2x^5+16x^4+25x³+40x²+75x These are the answer choices given to me, and neither me or my friend/classmate have been able to make much sense of this. If anyone out there can help, that would be awesome. Thanks, and have a great day! 
September 5th, 2011, 02:49 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,454 Thanks: 567  Re: Precalculus
Something is screwed up. When you multiply you get 4x^3  2x^2. f(g) leads to a rational function with both numerator and denominator has cubic polynomials.

September 5th, 2011, 03:04 PM  #3 
Senior Member Joined: Jun 2011 Posts: 154 Thanks: 0  Re: Precalculus
Wow..thank you for pointing that out. I've literally been doing math homework for 2 days straight, I think it's time for a break. But regardless, here is the CORRECT problem. I was trying to figure it out last night and couldn't. f(x) = 2x³5x g(x) = x²+8x+15 These are correct, I double checked twice, as well as the answer choices I gave in my original post. 
September 5th, 2011, 04:32 PM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,767 Thanks: 1016 Math Focus: Elementary mathematics and beyond  Re: Precalculus
It looks like f * g. (2x³  5x)(x² + 8x + 15) = 2x^5 + 16x^4 + 25x^3  40x^2  75x, choice number 3. 

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