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)

- anonymous

- chestercat

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- anonymous

- anonymous

- anonymous

Hey

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## More answers

- Keigh2015

do you have an idea for it yet?

- phi

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

- anonymous

so add 5x − 12 And 11x + 2

- phi

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

- Keigh2015

yes i believe

- phi

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

- anonymous

let me add the first one real quick hold on

- phi

can you do parts A and B?

- anonymous

16x−10

- phi

yes

- anonymous

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

- phi

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

- anonymous

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

- phi

too bad, I got the same thing.

- anonymous

is it?

- phi

yes, you did it correctlly

- anonymous

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

- anonymous

ooh yay okay

- phi

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.

- anonymous

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

- anonymous

- anonymous

- Keigh2015

that one confuses me too

- anonymous

- phi

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

- anonymous

@mathstudent55 i need help with part c

- phi

part C
f[g(x)]
first write down f(x)

- anonymous

5x − 12

- phi

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

- phi

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

- phi

can you replace g(x) in
5g(x) -12
with (11x+2)

- anonymous

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

- anonymous

- phi

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.

- anonymous

x=1\11 ? @phi

- phi

the right side is
5(11x + 2) -12
do 5 * 11x + 5*2 to distribute the 5
55x + 10 -12
now simplify 10-12

- anonymous

-2?

- phi

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

- anonymous

Yay thankyou @phi

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