<p>Ahhh I'm so terrible at functions and the most frustrating part is knowing that they're not that hard -__- Help me out please? </p>
<p>Question: </p>
<p>If f(x) = 4x-8 and g(x) = 3x² + 7, then g(f(3)) =
(A) 9
(B) 19
(C) 27
(D) 68
(E) 76</p>
<p>Oh & I have another question which isn't a function but I kinda of need a faster way to solve
this one: </p>
<p>Which of the following is equivalent to x²+ 4x + 3/ -3-x > 0 ? </p>
<p>(A) x<-1 and x is not = -3
(B) x> -1
(C) x> -1 and x is not equal to 3
(D) -3<x<-1 (e)="" x<="" -1="" or="" x="">3</x<-1></p>
<p>this is from PR isn’t it…</p>
<p>yes, you’ve caught me lol.</p>
<p>the first one is 55. there must be a typo.</p>
<p>That’s what I thought too because 68 didn’t make sense…</p>
<p>PR why you make so many typos…stressful…T___T</p>
<p>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.</p>
<p>the answer to the second one is A, but how did you get it?</p>
<p>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.</p>
<p>So either there’s another typo or I’m doing something wrong.</p>
<p>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]</p>
<p>(A) x<-1 and x is not = -3
(D) -3<x<-1
are left</p>
<p>The only way i way i would explain that D is incorrect is that if you plug in -2 for X. If you do that, the denominator is going to become negative which makes the whole expression negative and it would make the equation incorrect.</p>
<p>(A) x<-1 and x is not = -3
is left</p>
<p>plug in any number less than -1 and it will be correct.</p>
<p>(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). </p>
<p>(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.</p>
<p>Combine (1) and (2) to get x < -1 and x is undefined for x= -3. There are no other answers.</p>
<p>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.</p>