for f(x)=x^2+8 and g(x)=x^2-6 find a) (f*g)(x)
b) (g*f)(x) c. (f*g)(4)

Question

for f(x)=x^2+8 and g(x)=x^2-6 find a) (f*g)(x)
b) (g*f)(x) c. (f*g)(4)

anonymous · Answer

Is it: $$1\ f\circ g$$$$2\ f\times g$$$$3\ f\cdot g$$

anonymous · Answer

times in all of them

anonymous · Answer

Okay.  Do you know how to multiply the functions?

anonymous · Answer

$$x ^{2}+8 and g(x)=x ^{2}-6$$

anonymous · Answer

yes
there are three answers

anonymous · Answer

You know $f\times g = g\times f$.

anonymous · Answer

$$(f timesx)(x)$$

anonymous · Answer

So a and b are the same here.

anonymous · Answer

b. (g times f)(x)
c.  (f times g)(4)

anonymous · Answer

no they are switched a is for x^2-6 b is for x^2+8

anonymous · Answer

like a. answer is x^4-12x^2+44

anonymous · Answer

i just dont know how to do the problem

anonymous · Answer

Do you know how to multiply polynomials?  Like: $(x^2+8)(x^2-6)$

anonymous · Answer

yes

anonymous · Answer

So that didn't work?  I'm confused as to what you're struggling with.

anonymous · Answer

im having trouble of how is the answer 12x and 44

anonymous · Answer

The answer to which?

anonymous · Answer

for a x^4-12x^2+44

anonymous · Answer

Okay so what are the answers for a, b, and c     and what are you getting?  Did you write down the problem correctly?

anonymous · Answer

yes but i really dont know how to do them up to the end

anonymous · Answer

I'm getting for a and b, $x^4+2x^2-48$

anonymous · Answer

its say evaluate the exponential expression and simplify

anonymous · Answer

i came up with that to and its not right

anonymous · Answer

i$$x^4 +16x^2+58$$

anonymous · Answer

Then you must not have written the problem down correctly or something.  I don't know what to tell you.

hartnn · Answer

if the answer is x^4-12x^2+44
then it surely is 
(fog)(x)
and not times......

anonymous · Answer

oh thats why the times sign looks different its a o

anonymous · Answer

so how do i do that

anonymous · Answer

Remember my initial question?!  Look!  So it was 1 all along but you had me thinking it was 2, lol!

anonymous · Answer

im sorry

anonymous · Answer

You plug g(x)  into  f(x)

anonymous · Answer

yes i got tha(x^2-6)^2+8

anonymous · Answer

so $f(g(x)) = (x^2-6)^2+8$

anonymous · Answer

ok so do we times -6 with the power of 2 to get 12

anonymous · Answer

$f(g(x)) = (x^2-6)^2+8= (x^2-6)(x^2-6)+8$

anonymous · Answer

We have to use foil here to expand the $(x^2-6)^2$

anonymous · Answer

x^4+12x+36

anonymous · Answer

then add 8

anonymous · Answer

?

anonymous · Answer

It should be $-6x-6x = -12x$ not $+12x$

anonymous · Answer

oh duh -12x^2

anonymous · Answer

its midnight here and i havent slept in so long

anonymous · Answer

ok i have the answer to b. x^4+16x^2+58

anonymous · Answer

c. is 138

anonymous · Answer

omgosh thank you