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

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

11 answers

(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.
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
in addition -8+8=0 but when multiplied you get -64
(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
its the answer for B
Huh? You still want 49x^2-64
That is not 187
(7x-8)(7x+8) = (-14-8)(-14+8) = (-22)(-6) = 132
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) )
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...
so the book wrong?
Im not sure how they got 187.
okay so back track.
Get rid of my equation I had given. and lets go from there
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