Question

Given f(x) = 3x + 2 and g(x) = x2 + 4, find (g • f )(2).

Answer 1

do know what to do at all?

Answer 2

ok, so what you do is plug in the 2 for the value x.

Answer 3

you do this for both equations; f(x) and g(x).

Answer 4

then you multiply the results from both.

Answer 5

Oh, and btw, welcome to openstudy! :D

Answer 6

so for f(x):
f(x) = 3x + 2
f(x) = 3(2) + 2
f(x) = 6 + 2
f(x) = 8

for g(x):
g(x) = x^2 + 4
g(x) = (2)^2 + 4
g(x) = 4 + 4
g(x) = 8

then you multiply them together:
8*8 = your solution

Answer 7

hope this helps :D

Answer 8

(g • f )(x) = (3x + 2)(x^2 + 4)
= x^2(3x + 2) + 4(3x + 2)
= 3x^3 + 2x^2 + 12x + 8

(g • f )(2) = 3(2)^3 + 2(2)^2 + 12(2) + 8
= 3(8) + 2(4) + 24 + 8
= 24 + 8 + 24 + 8
= 24 + 24 + 8 + 8
= 48 + 16
= 64

Answer 9

that method works too... which is more conventional @Hero?

Answer 10

Well basically as a rule,

(g • f )(x) = g(x)f(x)

The question said to calculate (g • f )(2)
You computed g(2)*f(2)

They are both equivalent computations. One method seems "easier" to compute than the other.

Answer 11

ok :D thanks!

Answer 12

oh... i feel like a idiot. Ive done this before in class. I didn't recognize it here though. what is this called btw.

Answer 13

Operations on Functions:

(f + g)(x) = f(x) + g(x)
(f - g)(x) = f(x) - g(x)
(f • g)(x) = f(x) • g(x)
(f ÷ g)(x) = f(x) ÷ g(x)