Help with these 5 quick Pre-calculus questions?! Been stuck on these for ages!!!

- anonymous

Help with these 5 quick Pre-calculus questions?! Been stuck on these for ages!!!

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- anonymous

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- anonymous

@Hero @UnkleRhaukus @RyanL. @dape ANYONE

- dape

For the first one, simply subtract g from f.

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## More answers

- dape

In the second one \((g\circ f)(1)\) means \(g(f(1))\), so put 1 into f(x), you will get a number, put this number into g(x) and you get your answer.

- dape

#3, iterates means that you put the output of the function into the function again etc. You should start with \(x_0=0.1\), so calculate \(f(0.1)\), put this number into \(f(x)\), and that number into \(f(x)\) again etc. You will get a series of numbers which is the answer.

- dape

In #4 you should just add the functions. And in #5 you should put g(x) into f(x), which gives \((g\circ f)(x)\).

- anonymous

how would i do the first one? like i don't know how to subtract g from f.. @dape @Loser66 @skullpatrol

- dape

What is f(x) in #1?

- anonymous

9-x^2

- dape

Yes now subtract from that the expression for g(x).

- anonymous

so subtract 9-x^2 from 3-x?

- dape

The other way around, do \(9-x^2-(3-x)\)

- dape

Which is just \(f(x)-g(x).\)

- anonymous

how would i do that?

- Loser66

just subtract them as if you subtract 2 number, that's it.

- dape

Look at this video, it explains how you subtract polynomials. https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/addition-and-subtraction-of-polynomials

- anonymous

so would it be 6-x?

- Loser66

9-x^2-3+x=?

- anonymous

how can i subtract x^2 from 9? and would the second part be 3x?

- Loser66

if you can't , neither I. let them there!!

- dape

You should carefully watch the video I posted, it's kind of important that you learn how to manipulate polynomials to do these kinds of problems.

- anonymous

@sam

- anonymous

@aaronq @Hero @inkyvoyd @Loser66 @nincompoop @wolf1728 CAN ANYONE JUST HELP WITH 4 AND 5?! I REALLY NEED JUST THE ANSWER. I'VE BEEN STUCK ON THEM FOR 2 HOURS.

- anonymous

which one?

- anonymous

ooh nvm 4 and 5

- anonymous

\[f(x)=2x^2+8,g(x)=5x-6\]
\[f(x)+g(x)=2x^2+8+5x-6=2x^2+5x+2\] will work

- anonymous

So the answers would be 5x-6 and 2x^2+5x+2?

- anonymous

no, the answer is just \(2x^2+5x+2\)

- anonymous

for question number 4?

- anonymous

yes

- anonymous

okay, thanks! what about number 5?

- anonymous

\[f(x)\times g(x)=(x^2+8)(5x-6)\]

- anonymous

maybe you are supposed to multiply out

- anonymous

it looks like (f times g) (x)

- anonymous

yes exactly
multiply \(f(x)\) times \(g(x)\)

- anonymous

how would i do that

- anonymous

\[f(x)\times g(x)=(x^2+8)(5x-6)=5x^3-6x^2+40x-48\]

- anonymous

so i would simplify 5x^3-6x^2+40x-48 to get my answer?

- anonymous

how?

- anonymous

you have no like terms to combine, so there is nothing you can do with this

- anonymous

so is that my answer?

- anonymous

yes

- anonymous

no!

- anonymous

ok so that is the answer to number 5?

- anonymous

aw

- anonymous

i made a mistake because i copied it wrong
it is
\[f(x)\times g(x)=(2x^2+8)(5x-6)\]

- anonymous

so what is the answer?

- anonymous

you should get \(10 x^3-12 x^2+40 x-48\)

- anonymous

so is that the answer?

- anonymous

yes

- anonymous

ok
thank you!!! i may have a few more in a little

- anonymous

yw

- anonymous

can i have help with this last one and then i'm done. @satellite73

##### 1 Attachment

- anonymous

@satellite73 @Hero

- anonymous

\[g\circ f(4)=g(f(4))\] so the first step is to find \(f(4)\)
let me know what you get

- anonymous

the hint is a little weird, because the top says \(g\circ f(4)\) but then hint has \(g\circ f(-4)\)

- anonymous

i don't know how to do that though..

- anonymous

do you know how to find \(f(4)\) if \(f(x)=x^2+3\) ?

- anonymous

no

- anonymous

then you need to learn how to do it
where you see an \(x\) in \(x^2+3\) replace it by \(4\)

- anonymous

so it would be 4^2+3? which would be 19

- anonymous

yes

- anonymous

then since
\[f(4)=19\] you know
\[g(f(4))=g(19)\] now since
\[g(x)=\frac{x+5}{x}\] your job is to find \(g(19)\)

- anonymous

i.e. where you see \(x\) in \(\frac{x+5}{x}\) replace it by \(19\)

- anonymous

so it would be g(x) 19+5 over 19?

- anonymous

equals*

- anonymous

and that would be g(x) = 24/19 which is one of my answers. is that correct?

- anonymous

@satellite73

- anonymous

nevermind, it was right. i got it

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