Question

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

Answer 1

@Hero @UnkleRhaukus @RyanL. @dape ANYONE

Answer 2

For the first one, simply subtract g from f.

Answer 3

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.

Answer 4

#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.

Answer 5

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

Answer 6

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

Answer 7

What is f(x) in #1?

Answer 8

9-x^2

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

how would i do that?

Answer 14

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

Answer 15

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

Answer 16

so would it be 6-x?

Answer 17

9-x^2-3+x=?

Answer 18

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

Answer 19

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

Answer 20

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.

Answer 21

@sam

Answer 22

@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.

Answer 23

which one?

Answer 24

ooh nvm 4 and 5

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

for question number 4?

Answer 29

yes

Answer 30

okay, thanks! what about number 5?

Answer 31

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

Answer 32

maybe you are supposed to multiply out

Answer 33

it looks like (f times g) (x)

Answer 34

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

Answer 35

how would i do that

Answer 36

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

Answer 37

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

Answer 38

how?

Answer 39

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

Answer 40

so is that my answer?

Answer 41

yes

Answer 42

no!

Answer 43

ok so that is the answer to number 5?

Answer 44

aw

Answer 45

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

Answer 46

so what is the answer?

Answer 47

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

Answer 48

so is that the answer?

Answer 49

yes

Answer 50

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

Answer 51

yw

Answer 52

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

Answer 53

@satellite73 @Hero

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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

Answer 58

no

Answer 59

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

Answer 60

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

Answer 61

yes

Answer 62

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 \(g(19)\)

Answer 63

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

Answer 64

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

Answer 65

equals*

Answer 66

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

Answer 67

@satellite73

Answer 68

nevermind, it was right. i got it