Question

HELP!

Answer 1

@jim_thompson5910

Answer 2

Consider \[f(x)=x^2 +3x-70 \]

Answer 3

and \[g(x)=4(x-3)\]

Answer 4

plug x = 3 into f(x). What is the value of f(3) ?

Answer 5

wouldn't 3^2 +3(3) -70

Answer 6

yes

Answer 7

-52?

Answer 8

yes

Answer 9

ok and no idk what to do next

Answer 10

something with multiply g of x with f of x

Answer 11

\[\Large g({\color{red}{f(3)}})=g({\color{red}{-52}}) = ???\]

Answer 12

-220

Answer 13

correct

Answer 14

so that wraps up part B

Answer 15

part C is similar, just you work with g(x) first then move onto f(x)

Answer 16

i got 270

Answer 17

270 is correct for part C

Answer 18

for part D, you would use the idea that

\[\Large (f \circ g)(x) = f(g(x))\]

Answer 19

So that means

\[\Large (g \circ f)(-2) = g(f(-2))\]

Answer 20

-300?

Answer 21

ok now number 2 is so hard idk where to start i really need help

Answer 22

\(\LARGE (g \circ f)(-2) = -300\) is correct

Answer 23

`ok now number 2 is so hard idk where to start i really need help`
go ahead and post it

Answer 24

i did

Answer 25

oh nvm ill do it now

Answer 26

\[\Large (f \circ g)(x) = f(g(x))\]

using that idea, are you able to figure out what (f o g)(x) is equal to?

Answer 27

\[\Large f(x) = 3x\]
\[\Large f(x) = 3*(x)\]
\[\Large f({\color{red}{x}}) = 3*({\color{red}{x}})\]
\[\Large f({\color{red}{g(x)}}) = 3*({\color{red}{g(x)}}) \ ... \ \text{See Note 1}\]
\[\Large f({\color{red}{g(x)}}) = 3*({\color{red}{x^2+1}}) \ ... \ \text{See Note 2}\]
\[\Large f(g(x)) = ???\]


Note1: I replaced every copy of 'x' with 'g(x)' so the left side would have f(g(x))


Note2: On the right side, I replaced g(x) with x^2+1. This is because g(x) = x^2+1. In other words, the two expressions are equivalent or the same. Which is why this substitution is valid.

Answer 28

i got 9x^3 + 2

Answer 29

@jim_thompson5910

Answer 30

for f(g(x)) ?

Answer 31

no for the whole thing

Answer 32

Tell me what you got for f(g(x))

Answer 33

3x^2 +1

Answer 34

you didn't distribute properly

Answer 35

oh now I'm confused

Answer 36

3*(x^2+1) = ???

Answer 37

look back at my steps above to see how I got to 3*(x^2+1)

Answer 38

oh so 3x^2 +3

Answer 39

yes

Answer 40

now what is g(f(x)) equal to?

Answer 41

3x+1?

Answer 42

\[\Large g(x) = x^2+1\]
\[\Large g(x) = (x)^2+1\]
\[\Large g({\color{red}{x}}) = ({\color{red}{x}})^2+1\]
\[\Large g({\color{red}{f(x)}}) = ({\color{red}{f(x)}})^2+1\]
\[\Large g({\color{red}{f(x)}}) = ({\color{red}{3x}})^2+1\]
I'll let you simplify

Answer 43

9x^2 +1

Answer 44

yep, so we have

\[\Large f(g(x)) = (f \circ g)(x) = 3x^2+3\]
\[\Large g(f(x)) = (g \circ f)(x) = 9x^2+1\]

Answer 45

use that to compute
\[\Large (g \circ f)(x) - (f \circ g)(x)\]

Answer 46

-6x^2 +2

Answer 47

ok i have a couple more...

Answer 48

-6x^2 +2 is close but not correct

Answer 49

what did i do wrong

Answer 50

\[\Large (g \circ f)(x) - (f \circ g)(x)\]
\[\Large 9x^2+1-(3x^2+3)\]
\[\Large 9x^2+1-3x^2-3\]
\[\Large 6x^2-2\]

Answer 51

you subtracted in the wrong order

Answer 52

oh

Answer 53

can u help me with these?

Answer 54

Show me what you have so far

Answer 55

ok i already did number3... for number 4 i got x^2 +14x+48

Answer 56

number 4 has two parts

Answer 57

`for number 4 i got x^2 +14x+48`
was this for part A? or part B?