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

part A)
hint:
by definition, we have:
\[\Large \left( {a + b} \right)\left( x \right) = a\left( x \right) + b\left( x \right)\]

Answer 2

so would it be 5x+2

Answer 3

correct!

Answer 4

how would i go about doing the other ones?

Answer 5

part B)
again, by definition, we can write:
\[\Large \left( {a \cdot b} \right)\left( x \right) = a\left( x \right) \cdot b\left( x \right)\]

Answer 6

how would I do that

Answer 7

you have to multiply your function, like below:
\[\Large \left( {a \cdot b} \right)\left( x \right) = a\left( x \right) \cdot b\left( x \right) = \left( {3x + 10} \right) \cdot \left( {2x - 8} \right) = ...\]

Answer 8

functions*

Answer 9

so would it be 6x -80

Answer 10

@Michele_Laino

Answer 11

I got 6x^2-4x-80

Answer 12

I don't get it

Answer 13

you have to compute this:
\[\large \left( {a \cdot b} \right)\left( x \right) = a\left( x \right) \cdot b\left( x \right) = \left( {3x + 10} \right) \cdot \left( {2x - 8} \right) = ...\]
please use the "foil" method
Part C)
again, by definition, we get:
\[\large a\left\{ {b\left( x \right)} \right\} = 3\left\{ {b\left( x \right)} \right\} + 10 = 3 \cdot \left( {2x - 8} \right) + 10=...\]

Answer 14

so it would be 6x-14 right @Michele_Laino

Answer 15

thank you so much for your help!!! @Michele_Laino

Answer 16

:)