Question

Use the functions a(x) = 3x + 10 and b(x) = 2x − 8 to complete the function operations listed below.

Part A: Find (a + b)(x). Show your work. (3 points)

Part B: Find (a ⋅ b)(x). Show your work. (3 points)

Part C: Find a[b(x)]. Show your work. (4 points)

Answer 1

@JoannaBlackwelder

Answer 2

@triciaal

Answer 3

\[\large\rm \color{royalblue}{a(x) = 3x + 10},\qquad \color{orangered}{b(x) = 2x − 8}\]
\[\large\rm (a+b)(x)=\color{royalblue}{a(x)}+\color{orangered}{b(x)}\]\[\large\rm (a+b)(x)=\color{royalblue}{3x+10}+\color{orangered}{2x-8}\]Combine like-terms! :)

Answer 4

5x+2?

Answer 5

Yay good job!
That takes care of part A.

Answer 6

:}

Answer 7

For part B, you'll want to put some brackets around your a(x) and b(x) so the multiplication works out properly.\[\large\rm (a\cdot b)(x)=(\color{royalblue}{a(x)})\cdot(\color{orangered}{b(x)})\]\[\large\rm (a\cdot b)(x)=(\color{royalblue}{3x+10})\cdot(\color{orangered}{2x-8})\]

Answer 8

(3x+10)(2x+−8)
=(3x)(2x)+(3x)(−8)+(10)(2x)+(10)(−8)
=6x2−24x+20x−80
=6x2−4x−80

Answer 9

Correct?

Answer 10

Ooo looks good! :O

Answer 11

How bout part C, the composition.
Having any trouble with that one?

Answer 12

Yes thats actually the one i am confused on >_<

Answer 13

\[\large\rm a(\color{#DD4747}{x}) = 3\color{#DD4747}{x} + 10\]We're replacing all of the x's in our function a(x) with another function b(x).\[\large\rm a(\color{#DD4747}{b(x)}) = 3\color{#DD4747}{b(x)} + 10\]

Answer 14

But again, since we have some multiplication going on, let's place brackets around the b(x) before we plug it in.

Answer 15

\[\large\rm a(\color{#DD4747}{b(x)}) = 3(\color{#DD4747}{b(x)}) + 10\]\[\large\rm a(\color{#DD4747}{b(x)}) = 3(\color{#DD4747}{2x-8}) + 10\]

Answer 16

=(3)(2x)+(3)(−8)+10
=6x+−24+10
=6x+−24+10
=(6x)+(−24+10)
=6x+−14

Answer 17

yay good job!

Answer 18

i need help on part A!!!

Answer 19

@enchanted_bubbles

Answer 20

@zeddrix

Answer 21

@zepdrix

Answer 22

Then scroll up and read silly! :D

Answer 23

Notice the colors

Answer 24

Recall that addition is commutative, meaning we can move things around.
So \(\large\rm 3x+10+2x-8\)
is the same as
\(\large\rm 3x+2x+10-8\)

Combine your x's.
You have 3 of them, and 2 more of them.
3 apples + 2 apples = ?