For functions f(x) = 7x − 8 and g(x) = 7x + 8,

Question

find ⓐ (f · g)(x) ⓑ (f · g)(−2).
I have F(x)*G(x)= (7x-8)(7x+8).
I never really understood how this equation works. I can see the FOIL method but I don't quite understand it in this system of equations

Answer 1

(f · g) in this notation means "f follows g"
so (f · g)(x) = f( g(x) )
= f(7x + 8)
= 7(7x + 8) - 8
= 49x + 56 - 8
= 49x + 48
then f(-2) = 49(-2) + 48 = -50

another way:
g(-2) = 7(-2) + 8 =-6
then f(g(-2)) = f(-6) = 7(-6) - 8 = -42 - 8 = -50
which verifies my answer above

It does not mean multiplication like you had it.

Answer 2

I'm not sure, I'm following what you are saying. I should've got (f*g)(x)=49x^2-64 for A and for B is (f*g)(-2)=187.
I got (7x-8)(7x+8)=49x^2-64

Answer 3

in addition -8+8=0 but when multiplied you get -64

Answer 4

(f*g)(x)=49x^2-64
(f*g)(-2)=49*4-64 = 196-64 = 132
How did you get 187? That's 4x^2-9

Answer 5

its the answer for B

Answer 6

Huh? You still want 49x^2-64
That is not 187
(7x-8)(7x+8) = (-14-8)(-14+8) = (-22)(-6) = 132

Answer 7

You didn't read what I said very carefully.

the notation f ∘ g does NOT mean multiplication
it means "f follows g", that is, do the g(x) function first, then
put that result into the f(x) function

Again, look carefully at my response, I did it two ways, both gave
me the same answer.

You were treating it like a multiplication

Again, f(x)*g(x) = (7x-8)(7x+8) <---- this is what you did
but you have to do (f ∘ g)(x) = f( g(x) )

Answer 8

well, he said (f · g), not (f ∘ g)
Usually the dot just means multiplication.

But one way or the other, it should be clear by now...

Answer 9

so the book wrong?

Answer 10

Im not sure how they got 187.

Answer 11

okay so back track.
Get rid of my equation I had given. and lets go from there