Question

For the functions given, find a) (f*g)(x) b) (f*g)(2)
f(x)=x-3, g(x)=x+6

a) (f*g)(x) = ?
b) (f*g)(2)= ?

Answer 1

so, multiply them then

Answer 2

so here, you literally just plug in those functions wherever you see f(x) and g(x)

example

(f*g)(x)
you have an f(x), and you have a g(x)...plug them in

(x - 3) * (x + 6)

can you do this?

Answer 3

x^2+3x-18?

Answer 4

correct...that would be your a)

now for b) you have (f*g)(2) ....notice how the (2) is where the (x) was before....so what do you think you do with that 2?

Answer 5

so it is written (x-3)*(x+6)(2)?

Answer 6

no not quite...where you see that (2) is exactly where you saw the (x) ....did you write the other one as
(x-3)*(x+6)(x)? no because that wouldn't have worked.

instead you used that (x) and you plugged it in for every x you saw in the equation a.k.a

(x - 3)*(x + 6) **same right?

so now....you would plug (2) in for EVERY "x" you see in the equation you derived from finding (f*g)(x)

remember how you had gotten

x² + 3x - 18

now...you would plug 2 into that equation wherever you see an "x"

Answer 7

So then... it would be (2)^2+3(2)-18 =

Answer 8

= -8?

Answer 9

correct! :)

Answer 10

Thank you so much :)

Answer 11

no problem!