Question

Hi I'm new to open study, If someone could please help me with these 3 questions. I cant seem to get them right.

1) Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) :

f(x) = 3x2 + 2

g(x) = x − 8

2) Given the following functions f(x) and g(x), solve f[g(10)]

f(x) = 10x + 8

g(x) = x + 9

3) Given the following functions f(x) and g(x), solve (f + g)(3)

f(x) = 2x + 21

g(x) = x − 24

Answer 1

(f ⋅ g)(2) is short for

f(2) * g(2)

can you find f(2) ?

Answer 2

I have no idea how to start.

Answer 3

they give you a formula
f(x) = 3x^2 + 2

f(x) is the "short name" and 3x^2 + 2 is the formula

f(2) means: find the formula, find the "x" in the formula and replace the x with a 2
can you do that?

Answer 4

So 3(2)^2+2?

Answer 5

38?

Answer 6

yes. now simplify that

Answer 7

Is it 38?

Answer 8

no. how did you get that?
remember order of operations

first do exponents, so first do 2^2

Answer 9

2^2 means 2*2

Answer 10

Well I replaced the x with 2. And the formula is 3x^2 + 2. Is it 16?

Answer 11

3 times 4 is 12 and 12 plus 2 is 14. Sorry 14?

Answer 12

it is worth knowing how to do this.
3*2^2 +2

first do 2^2 which is 2*2 . you get 4
so you have
3*4 +2
12+2
14

yes 14

Answer 13

(f ⋅ g)(2) is short for f(2) * g(2)
so far we have f(2) is 14

now we need g(2)
can you do that ?

Answer 14

Where do I start?

Answer 15

to find g(2)
find the formula for g
replace any x's in the formula with 2
simplify

Answer 16

How do I find the formula for g?

Answer 17

Oh they gave me the formula

Answer 18

g(x) = x − 8

Answer 19

they give it to you.
g(x) is the "name" they give to x-8
that is what
g(x) = x − 8
means

Answer 20

So g(2)=2-8

Answer 21

yes, and that simplifies to what?

Answer 22

g(2)=-6

Answer 23

ok now we have
(f ⋅ g)(2) is short for f(2) * g(2) so far we have f(2) is 14 and g(2) is -6
now we multiply to get the final answer

Answer 24

14*-6=-84

Answer 25

yes.

Answer 26

Thankyou! Can you help with the other 2?

Answer 27

Let's skip to Q3
(f + g)(3)

f(x) = 2x + 21

g(x) = x − 24


can you guess what (f+g)(3) is short for ? (based on the first question)

Answer 28

f(3) and g(3)

Answer 29

it would be better to say f(3) + g(3)

Answer 30

f(3)=2(3)+21
f(3)=27?

Answer 31

yes

Answer 32

So g(x) = x − 24
g(3)=3-24
g(3)= -21?

Answer 33

yes

Answer 34

And 27*-21 is -567

Answer 35

ok, but we are doing (f + g)(3) = f(3) + g(3)

Answer 36

Ok so what do we do know that we know what f and g are?

Answer 37

the + means add

Answer 38

27+(-21)=6

Answer 39

yes. notice in Q1 we have multiply (that is what the dot means)
and in this question we are adding
we might also see (f-g)(3)
(subtract)
or
(f/g)(3)
divide

Answer 40

now Q2
this one is a bit different. The formulas are not combined using add or multiply
we have something called "composition"
(they have to call it something)

Answer 41

Im still stuck on 3

Answer 42

My answer choices are:
98
198
190
2052

Answer 43

those are the choices for
(f + g)(3) where
f(x) = 2x + 21
g(x) = x − 24

??

Answer 44

Yes

Answer 45

those look like the choices for Q2 which we have not done yet

Answer 46

Oh Im sorry I got confused

Answer 47

The answer was 6 sorry

Answer 48

Ok we can do #3 now

Answer 49

Q2

solve f[g(10)]
f(x) = 10x + 8
g(x) = x + 9

think of g(10) as some number (which it is)
let's find g(10)
can you do that ?

Answer 50

Ok so g(10)=10+9?

Answer 51

yes, and that simplifies to 19

so g(10) is 19

if we replace g(10) with 19 in
f[g(10)] we get f(19)
(the [ vs ( is just to make it easier to read in f[g(10)] ... but it means the same as parens)

anyway
we have figured out that
f[g(10)] is the same as f(19)

now we need to find f(19)

Answer 52

f(x) = 10x + 8
So f(19)=10(19)+8?

Answer 53

ok, and what number do you get?

Answer 54

you do 10 times 19
then add 8

Answer 55

198?

Answer 56

Thankyou so so much. I got a 100%! I havent gotten a 100% before. You're a really good tutor!