For f(x) = x^2+4 and g(x)=x^2-2, how would you find (f*g)(x), (g*f)(x), and (f*g)(4)? https://i.imgur.com/zS0XkTh.png

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.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

For f(x) = x^2+4 and g(x)=x^2-2, how would you find (f*g)(x), (g*f)(x), and (f*g)(4)? https://i.imgur.com/zS0XkTh.png

Mathematics
See more answers at brainly.com
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.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

for (f o g) (x) that means to plug in the g(x) function for every x you find in the f(x) so it should look like \[\large ( f \cdot g)(x) = (x^2-2)^2+4\] then just expand the left part of the equation you need this part before you can evaluate the result when x = 4 for (g o f ) (x) it means plug in your f(x) equation for all x's inside the g(x) function so we have something like this \[( g \cdot f)(x) = (x^2+4)^2-2\]
So @UsukiDoll, after writing out the first one you can just substitute 4 for X and get something like this? (4^2-2)^2 +4 which is (16-2)^2 +4 which becomes (14^2) +4 then then so on, Which gives me 200, so 200 would be the answer for C?
Your question is asking for parts.. like for part a evaluate when we have (f o g )(x) and then we need that result to answer part c which is evaluate when x=4..

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Right, which is why I substituted 4 as X into the answer to the first one.
ah. I see.. so we can just leave this unexpanded when x = 4
\[\large ( f \cdot g)(4) = (4^2-2)^2+4\] \[\large ( f \cdot g)(4) = (16-2)^2+4\] \[\large ( f \cdot g)(4) = (14)^2+4\] \[\large ( f \cdot g)(4) = 196+4=200\] I got 200 too.
So a is (f⋅g)(x)=(x2−2)2+4, b is (g⋅f)(x)=(x2+4)2−2, and the last is 200. Thanks, this was waaay lass complicated then I thought it would be. I think I got it, lemme know if I'm missing something!
I think we need to expand a bit for a and b...
\[( g \cdot f)(x) = (x^2+4)(x^2+4)-2\] \[\large ( f \cdot g)(x) = (x^2-2)(x^2-2)+4\]
do you know FOIL?
the first outer inner last.
I'm supposed to simplify final answers, but I guess those aren't final. I know how to foil and distribute, yes.
\[( g \cdot f)(x) = (x^2)(x^2)+4(x^2)+4(x^2)+4(4)-2\] <-
(x2−2)(x2−2)+4 can simplify to (x^2-4) x^2+8, right?
and for the other one \[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4\]
whoa one at a time XD
okay okay xD
\[( g \cdot f)(x) = x^4+8(x^2)+16-2\] when you distributed/used foil/ and simplified you got up until this step right?
\[( g \cdot f)(x) = x^4+8(x^2)+14\]
did you get this result for part b when you did foil?
For part b I got to this, so yes! (g . f)(x) = x^4+8(x^2)+14
alright so let's get part a \[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x)+(-2x)+(-2)(-2)+4 \]
\[\large ( f \cdot g)(x) = x^4-4x^2+4+4\] made a mistake on my latex. CAREFUL!
Simplifying that gives me 2x^2 + -2x^2 -8.
wait oops
-_- do that again.
\[\large ( f \cdot g)(x) = (x^2)(x^2)+(-2x^2)+(-2x^2)+(-2)(-2)+4\]
\[\large ( f \cdot g)(x) = x^4-4x^2+4+4 \]
\[\large ( f \cdot g)(x) = x^4-4x^2+8\]
Right, I missed the positive 8 and didn't distribute one of the 2 I think. So x^4−4x^2+8 is A.
yeah
Wait a minute, for part b if you substitute 4 now into x^4+8(x^2)+14 I get 398 instead of 200.
umm for part c you need the result from part a
I'm an idiot. I get 200.
a and c are related to each other .... so we obtain the result from part a to answer part c which was 200
I got confused for a second and got mixed up. Oop.
Thanks for the help, I think I got it now. :D

Not the answer you are looking for?

Search for more explanations.

Ask your own question