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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

Algebra
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  • phi
(f ⋅ g)(2) is short for f(2) * g(2) can you find f(2) ?
I have no idea how to start.
  • phi
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?

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Other answers:

So 3(2)^2+2?
38?
  • phi
yes. now simplify that
Is it 38?
  • phi
no. how did you get that? remember order of operations first do exponents, so first do 2^2
  • phi
2^2 means 2*2
Well I replaced the x with 2. And the formula is 3x^2 + 2. Is it 16?
3 times 4 is 12 and 12 plus 2 is 14. Sorry 14?
  • phi
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
  • phi
(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 ?
Where do I start?
  • phi
to find g(2) find the formula for g replace any x's in the formula with 2 simplify
How do I find the formula for g?
Oh they gave me the formula
g(x) = x − 8
  • phi
they give it to you. g(x) is the "name" they give to x-8 that is what g(x) = x − 8 means
So g(2)=2-8
  • phi
yes, and that simplifies to what?
g(2)=-6
  • phi
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
14*-6=-84
  • phi
yes.
Thankyou! Can you help with the other 2?
  • phi
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)
f(3) and g(3)
  • phi
it would be better to say f(3) + g(3)
f(3)=2(3)+21 f(3)=27?
  • phi
yes
So g(x) = x − 24 g(3)=3-24 g(3)= -21?
  • phi
yes
And 27*-21 is -567
  • phi
ok, but we are doing (f + g)(3) = f(3) + g(3)
Ok so what do we do know that we know what f and g are?
  • phi
the + means add
27+(-21)=6
  • phi
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
  • phi
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)
Im still stuck on 3
My answer choices are: 98 198 190 2052
  • phi
those are the choices for (f + g)(3) where f(x) = 2x + 21 g(x) = x − 24 ??
Yes
  • phi
those look like the choices for Q2 which we have not done yet
Oh Im sorry I got confused
The answer was 6 sorry
Ok we can do #3 now
  • phi
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 ?
Ok so g(10)=10+9?
  • phi
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)
f(x) = 10x + 8 So f(19)=10(19)+8?
  • phi
ok, and what number do you get?
  • phi
you do 10 times 19 then add 8
198?
Thankyou so so much. I got a 100%! I havent gotten a 100% before. You're a really good tutor!

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