Question

Use the functions f(x) = 5x − 12 and g(x) = 11x + 2 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

@Keigh2015

Answer 2

@phi

Answer 3

Hey

Answer 4

do you have an idea for it yet?

Answer 5

(f + g)(x)

that is short of adding f(x) + g(x)

Answer 6

so add 5x − 12 And 11x + 2

Answer 7

and f(x)+g(x) is short for: write down the "formula" for f(x) and add it to the "formula" for g(x)

yes

Answer 8

yes i believe

Answer 9

B is the same idea except you multiply (use FOIL to multiply it out)

Answer 10

let me add the first one real quick hold on

Answer 11

can you do parts A and B?

Answer 12

16x−10

Answer 13

yes

Answer 14

Yea i think so, ill try could you check my work?

Answer 15

for part C
f[g(x)]
means "in the formula for f(x), replace "x" with g(x)"

Answer 16

for part B i got 55x2−122x−24 i think thats wrong

Answer 17

too bad, I got the same thing.

Answer 18

is it?

Answer 19

yes, you did it correctlly

Answer 20

ill just put that as the answer, because i honestly have to clue.

Answer 21

ooh yay okay

Answer 22

you can check that it is correct. pick a number for x, such as 1
then f(x) = 5x − 12 at x=1 is 5-12= -7
and g(x) = 11x + 2 at x=2 is 11+2 = 13
and -7*13= -91

now use your formula
55x^2−122x−24 at x=1... you get 55 -122 -24 = -91
same number.

that does not prove it, but if you did that for a few values, and it always works, it probably is correct.

Answer 23

for part c, questions like that confuse me cause i never learned the foil method.

Answer 24

@phi

Answer 25

@Keigh2015

Answer 26

that one confuses me too

Answer 27

@mathstudent55

Answer 28

but if you FOIL it:
( 5x − 12) (11x+2)

F first: 5x*11x = 55x^2
O outer: 5x*2 = 10x
I inner: -12*11x = -132x
L last: -12*2 = -24
combine the two middle terms 10x-132x = -122 x
and the answer is
55x^2 -122x -24

Answer 29

@mathstudent55 i need help with part c

Answer 30

part C
f[g(x)]

first write down f(x)

Answer 31

5x − 12

Answer 32

like this
f(x)=5x − 12

we want f[g(x)]
that means erase the x and replace it with g(x)

erase and replace:
f( g(x) ) = 5g(x) -12

Answer 33

then replace g(x) with g(x)'s formula (11x + 2)
be sure to use the parens

Answer 34

can you replace g(x) in
5g(x) -12

with (11x+2)

Answer 35

f( 11x + 2) = 5(11x + 2) -12

Answer 36

@phi

Answer 37

yes, but we usually leave the left side in "short form" f(g(x))
and only expand the right side
but yes that looks good.

you can distribute the 5 (multiply 5 times each thing inside the parens)
and simplify the right side a little.

Answer 38

x=1\11 ? @phi

Answer 39

the right side is
5(11x + 2) -12

do 5 * 11x + 5*2 to distribute the 5
55x + 10 -12
now simplify 10-12

Answer 40

-2?

Answer 41

yes. so part C is
f[g(x)]= 55x-2

Answer 42

Yay thankyou @phi