SOLUTION: How do you solve this problem f[g(-2)] ?

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Question 253855: How do you solve this problem f[g(-2)] ?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
assume the following as an example:

f(x) = x^2

g(x) = 3x+2

you want to find (f(g(-2))

start with g(x) = 3x+2

you want to find g(-2).

replace x with (-2) to get:

g(-2) = 3*(-2) + 2 = -6 + 2 = -4

you have g(-2) = -4

now you want to find f(g(-2)).

start with f(x) = x^2

replace x with g(-2) to get:

f(g(-2)) = (g(-2))^2

since g(-2) = -4, then replace g(-2) with -4 to get:

f(-4) = (-4)^2 = 16

you have f(g(-2)) = 16

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Here's another example.

let f(x) = sqrt(x)

let g(x) = x^3 + 3x^2 - 5

you want to find f(g(3))

first thing you want to do is find g(3).

since g(x) = x^3 + 3x^2 - 5, you replace x with 3 to get:

g(3) = (3)^3 + 3*(3)^2 - 5 = 27 + 27 - 5 = 49.

you now want to find f(g(3))

start with f(x) = sqrt(x).

replace x with g(3) to get:

f(g(3)) = sqrt(g(3))

since g(3) = 49, then replace g(3) with 49 to get:

f(49) = sqrt(49) = 7.

you have f(g(3)) = 7

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to keep this in the abstract, here's what's happening.

let f(x) = 5*x

let g(x) = 2*x

you want f(g(x)).

look at f(x) = 5*x

replace x with g(x) to get:

f(g(x)) = 5*(g(x))

since g(x) = 2*x, then replace g(x) with 2*x to get:

f(2*x) = 5*(2*x) = 10*x

if you are still having problems, send me your equation and I'll solve it for you to show you how it's done.

if you have any questions, send them to me and I'll answer them as best I can.

you also might want to look at the following link.

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut30b_operations.htm