At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
(f ⋅ g)(2) is short for f(2) * g(2) can you find f(2) ?
I have no idea how to start.
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?
yes. now simplify that
Is it 38?
no. how did you get that? remember order of operations first do exponents, so first do 2^2
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?
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
(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?
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
they give it to you. g(x) is the "name" they give to x-8 that is what g(x) = x − 8 means
yes, and that simplifies to what?
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
Thankyou! Can you help with the other 2?
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)
it would be better to say f(3) + g(3)
So g(x) = x − 24 g(3)=3-24 g(3)= -21?
And 27*-21 is -567
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?
the + means add
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
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
those are the choices for (f + g)(3) where f(x) = 2x + 21 g(x) = x − 24 ??
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
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?
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?
ok, and what number do you get?
you do 10 times 19 then add 8
Thankyou so so much. I got a 100%! I havent gotten a 100% before. You're a really good tutor!