SOLUTION: Find the composition function f(g(x)) f(u)=3u^2+3u-4 and g(x)=x+1 f(g(x)) =? Please help I keep getting it wrong. Not sure what I am doing wrong since I substitute "x+1" f

Algebra ->  Functions -> SOLUTION: Find the composition function f(g(x)) f(u)=3u^2+3u-4 and g(x)=x+1 f(g(x)) =? Please help I keep getting it wrong. Not sure what I am doing wrong since I substitute "x+1" f      Log On


   

Question 896678: Find the composition function f(g(x))
f(u)=3u^2+3u-4 and g(x)=x+1
f(g(x)) =?
Please help I keep getting it wrong. Not sure what I am doing wrong since I substitute "x+1" for every "u" and distribute. Any help will be greatly appreciated and thank you!
Found 2 solutions by thesvw, Theo:
Answer by thesvw(77) About Me  (Show Source):
You can put this solution on YOUR website!
Yes you're doing right.
f%28u%29+=+3u%5E2+%2B+3u+-4
g%28x%29+=+x%2B1
f%28g%28x%29%29+=+y+=+3%28x%2B1%29%5E2+%2B+3%28x%2B1%29+-+4
y+=+3x%5E2+%2B6x+%2B+3+%2B3x+%2B3+-4
y+=+3x%5E2+%2B+9x+%2B+2

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
that's what you should be doing as far as i can see.
let me see what i can get and we can compare notes.

you have:

g(x) = x + 1

f(u) = 3u^2 + 3u - 4

to find f(g(x)), you replace u with x+1 and evaluate.

you get:

f(g(x)) = 3(x+1)^2 + 3(x+1) - 4 which becomes:

f(g(x)) = 3(x^2 + 2x + 1) + 3x + 3 - 4 which becomes:

f(g(x)) = 3x^2 + 6x + 3 + 3x + 3 - 4

combine like terms to get:

f(g(x)) = 3x^2 + 9x + 2

that's your solution.

an easy way to check it out is as follows:

let x = 3 (any value of x chosen at random will do)

g(x) = 3+1 = 4

f(4) = 3*4^2 + 3*4 - 4 = 48 + 12 - 4 = 56

now go to your final equation and solve using x = 3

f(g(x)) = 3x^2 + 9x + 2 becomes:

f(g(3)) = 3*3^2 + 9*3 + 2 which becomes:

f(g(3)) = 3*9 + 27 + 2 which becomes:

f(g(3)) = 27 + 27 + 2 which becomes:

f(g(3)) = 56

both the original equations and the final equations give you the same answer so you're good.