Question

Use the functions f(x) = 4x − 5 and g(x) = 3x + 9 to complete the function operations listed below.

Part A: Find (f + g)(x). Show your work. (3 points)

Part B: Find (f ⋅ g)(x). Show your work. (3 points)

Part C: Find f[g(x)]. Show your work. (4 points)

Answer 1

Hint for Part A:
(f + g)(x) = f(x) + g(x)

Answer 2

@AnimeGhoul8863 any thoughts on this?

Answer 3

(f+g)(x)=4x-5+3x+9
Then i think we switch them so it looks like
4x-5+3x+9=(f+g)(x)
then we group the like terms so it looks like
4x+3x-5+9
Then........
AM i right so far?

Answer 4

Looks good so far.

Answer 5

I should say though it's best that you get used to writing it in this format:
\(\begin{align*}
(f + g)(x)
&= f(x) + g(x)\\
&=(4x - 5) + (3x + 9) \\
&=(4x + 3x) + (9 - 5)\\

\end{align*}\)

Answer 6

Then we separate them so it looks like
4x+3x=7x
so its
7x-5+9
Then we add and subtract
-5+9=4
so we have
7x+4
Then we urmm......i think we subtract each side by 4
and then we simplify
7x=f+g-4
then im stuck here.......e.e

Answer 7

You should have stopped at \(7x + 4\):
Because if you continued with the way I started showing you above you would have ended with
\(\begin{align*}
(f + g)(x)
&= f(x) + g(x)\\
&=(4x - 5) + (3x + 9) \\
&=(4x + 3x) + (9 - 5)\\
&=7x + 4
\end{align*}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 8

That is the correct format to write these.

Answer 9

oh

i cant use this format qc gives us on my school

Answer 10

Yes you can.

Answer 11

You can at least write it down on paper or on your tablet

Answer 12

hero ive done this all year and its what my teacher told us to do i cant do that format i just have to do it the way i do it now

Answer 13

Your teacher is wrong. There's only one correct way to do it.

Answer 14

So Part A:
(f+g)(x)=4x-5+3x+9
Then i think we switch them so it looks like
4x-5+3x+9=(f+g)(x)
then we group the like terms so it looks like
4x+3x-5+9
Then we separate them so it looks like
4x+3x=7x
so its
7x-5+9
Then we add and subtract
-5+9=4
so we have
7x+4

Answer 15

That's a silly way to do it. What I did above is the correct way.

Answer 16

This is literally copy and paste what i did above that you said was correct

Answer 17

What you did is correct, just not the most efficient way.

Answer 18

If your teacher isn't teaching the efficient way to do these, then I don't agree with her methodology.

Answer 19

im home schooled so i cant do those symbols or that format

Answer 20

(f + g)(x) = f(x) + g(x) is standard notation

Answer 21

ok

Answer 22

Just like
\((f \cdot g)(x) = f(x)g(x)\)

Answer 23

ok

Answer 24

thats what i did
\(\color{#0cbb34}{\text{Originally Posted by}}\) @AnimeGhoul8863
So Part A:
(f+g)(x)=4x-5+3x+9 <<

Answer 25

(f+g)(x)=4x-5+3x+9
Then i think we switch them so it looks like
(4x-5)+(3x+9)=(f+g)(x)
then we group the like terms so it looks like
=(4x+3x)(-5+9)
Then we separate them so it looks like
=(4x+3x)=7x
so its
=(7x-5+9)
Then we add and subtract
=(-5+9)=4
so we have
=(7x+4)

Answer 26

^^this what you want it to look like ????

Answer 27

Cause if you look at yours thats "correct" it has () around it so thats what i did \(\color{#0cbb34}{\text{Originally Posted by}}\) @Hero
You should have stopped at \(7x + 4\):
Because if you continued with the way I started showing you above you would have ended with
\(\begin{align*}
(f + g)(x)
&= f(x) + g(x)\\
&=(4x - 5) + (3x + 9) \\
&=(4x + 3x) + (9 - 5)\\
&=7x + 4
\end{align*}\)
\(\color{#0cbb34}{\text{End of Quote}}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 28

Parentheses are not necessary for the last step.

Answer 29

(f+g)(x)=4x-5+3x+9
Then i think we switch them so it looks like
(4x-5)+(3x+9)=(f+g)(x)
then we group the like terms so it looks like
=(4x+3x)(-5+9)
Then we separate them so it looks like
=(4x+3x)=7x
so its
=(7x-5+9)
Then we add and subtract
=(-5+9)=4
so we have
=7x+4

So this^

Answer 30

Ok now part B

Answer 31

(f+g)(x)=4x-5*3x+9

Answer 32

If you do it properly you write
\((f \cdot\ g)(x) = f(x)g(x)\)

What you wrote above mixes sums with multiplication

Answer 33

i thought we were doing multiplication

Answer 34

but ok let me try

Answer 35

We are but is \((f + g)(x)\) a sum or a multiplication?

Answer 36

That's why you should use the notation that I gave you above.

Answer 37

Sum of Two Functions
\((f + g)(x) = f(x) + g(x)\)

Multiplication of Two Functions
\((f \cdot\ g)(x) = f(x)g(x)\)

Answer 38

ok

Answer 39

(f . g)(x)=(4x-5)(3x+9)
then i think we distribute it so it looks like
=4x * 3x + 4x * 9 - 5 * 3x - 5 * 9 ........e.e i think
then we simplify it
(fg)=12x^2 + 21x - 45
Switch sides
12x^2 + 21x - 45=(fg)
And now im stuck e.e

Answer 40

@Hero

Answer 41

\(\begin{align*}(f \cdot\ g)(x)&=f(x)g(x) \\
&=(4x-5)(3x+9)\\
&=4x(3x + 9) - 5(3x + 9)\\
&=12x^2 + 36x - 15x - 45\\
&=12x^2 + 21x - 45
\end{align*}\)

Answer 42

Correct

Answer 43

Don't know what's going on with the side switching but I assure you that you don't have to do it like that. It's not necessary.

Answer 44

so i dont have to explain what im doing

Answer 45

ok then i wont
Part C now

Answer 46

now this one i really have no clue on solving

Find f[g(x)]. Show your work.

Answer 47

@Hero

Answer 48

Yes, with \(f(g(x)\) you put the entire expression for g(x) as the input to f(x):

\(f(g(x)) = f(3x + 9) \)

Answer 49

Then you evaluate \(f(3x + 9)\). Which all that means is you have an expression as the input to \(f(x)\) rather than a number.

So \(f(3x + 9) = 4(3x + 9) - 5\)

Then you finish simplifying the right hand side.

Answer 50

The correct sequence of steps are as follows:
\(\begin{align*}
f(g(x)) &= f(3x + 9)\\
&=4(3x + 9) - 5\\
&=12x + 36 - 5\\
&=12x + 31
\end{align*}\)

Answer 51

Thank you