6thstation

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) -3<x<-1
(E) x< -1 or x>3

hgsoloco

this is from PR isn't it....

6thstation

yes, you've caught me lol.

parthp1128

the first one is 55. there must be a typo.

realityisadream

^ you are right

6thstation

That's what I thought too because 68 didn't make sense...

PR why you make so many typos...stressful...T___T

jacobo2880

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.

6thstation

the answer to the second one is A, but how did you get it?

kestrel24

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.

parthp1128

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<x<-1
are left

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.

(A) x<-1 and x is not = -3
is left

plug in any number less than -1 and it will be correct.

fogcity

(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.