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 08-25-2011, 10:10 PM #1 Junior Member   Join Date: Jul 2011 Posts: 36 Functions Help Ahhh I'm so terrible at functions and the most frustrating part is knowing that they're not that hard -__- Help me out please? Question: If f(x) = 4x-8 and g(x) = 3x² + 7, then g(f(3)) = (A) 9 (B) 19 (C) 27 (D) 68 (E) 76 Oh & I have another question which isn't a function but I kinda of need a faster way to solve this one: Which of the following is equivalent to x²+ 4x + 3/ -3-x > 0 ? (A) x<-1 and x is not = -3 (B) x> -1 (C) x> -1 and x is not equal to 3 (D) -33 Reply
 08-25-2011, 10:12 PM #2 Member   Join Date: Aug 2011 Posts: 369 this is from PR isn't it.... Reply
 08-25-2011, 10:24 PM #3 Junior Member   Join Date: Jul 2011 Posts: 36 yes, you've caught me lol. Reply
 08-25-2011, 10:24 PM #4 Member   Join Date: Aug 2011 Posts: 305 the first one is 55. there must be a typo. Reply
 08-25-2011, 10:26 PM #5 Member   Join Date: Aug 2011 Posts: 360 ^ you are right Reply
 08-25-2011, 10:32 PM #6 Junior Member   Join Date: Jul 2011 Posts: 36 That's what I thought too because 68 didn't make sense... PR why you make so many typos...stressful...T___T Reply
 08-26-2011, 12:05 AM #7 Junior Member   Join Date: Feb 2011 Location: 北弗吉尼亚 --> 南カリフォルニ Posts: 159 Wow, I almost died when I didn't see 55 in the options. I think the answer to the second one is A but I don't have a calc or a piece o' paper so I am not sure atm. Reply
 08-26-2011, 01:57 PM #8 Junior Member   Join Date: Jul 2011 Posts: 36 the answer to the second one is A, but how did you get it? Reply
 08-26-2011, 02:25 PM #9 Junior Member   Join Date: Jul 2011 Posts: 133 Factor the numerator to get (x+3)(x+1) / (-3-x). X can't be -3 because that would cause the denominator to be 0. Then you solve by multiplying (-3-x) --> (x+3)(x+1) > 0. That means that x>-3 or x>-1. But I'm not sure how to get x<-1. In fact, that shouldn't be the answer. If you plug in -2 you get (-2+3)(-2+1)=-1, which is <0. So either there's another typo or I'm doing something wrong. Reply
 08-26-2011, 03:23 PM #10 Member   Join Date: Aug 2011 Posts: 305 x²+ 4x + 3/ -3-x > 0 = (x+3)(x+1) / -(x+3) > 0 ->x can not equal to -3 or -1 because it would make the numerator equal 0. (the question is asking that the fraction must be greater than 0) [you can elliminate B,C, and E] (A) x<-1 and x is not = -3 (D) -3
 08-26-2011, 08:12 PM #11 Senior Member   Join Date: Nov 2009 Posts: 2,026 (1) Before considering the inequality simplify the expression. Factor the numerator, and you get: x²+ 4x + 3/(-3-x) = (x+3)(x+1) / (- (x+3) ) which is "undefined" (equal to 0/0) when x = - 3. It's defined for all other values of x, and it simplifies to -(x+1). (2) Now apply the inequality to the simplified expression to get -(x+1) > 0. Rewrite (multiply both sides of the inequality by -1) as x+1 < 0. Solve that to get x< - 1. Combine (1) and (2) to get x < -1 and x is undefined for x= -3. There are no other answers. You can also solve problems like this by "substitutions" with the goal of eliminating options. Try for x a negative number less than -3, and note that it satisfies the inequality so this eliminates D. Note that in the post above the choice x = -2 is used to eliminate D. However the computation is incorrect for x = -2. It is a valid solution, as are all values less than -1. But D says the numbers MUST be in the range -1 to -3. Reply

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