SOLUTION: i am stuck on the following hw problem. included is a pic of the problem http://imgur.com/IPhMu79 any help would be appreciated

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Question 921683: i am stuck on the following hw problem. included is a pic of the problem
http://imgur.com/IPhMu79
any help would be appreciated
Found 2 solutions by Theo, KMST:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
f(x) = |x-38|

g(x) = -13x+5

find (g o f)(x)

simplify your answer.

(g o f) = g(f(x)) = g(|x-38|) = -13 * |x-38| + 5

i don't believe it can be simplified any further than that.

you can test to see if the equation holds true by picking a value for x and then working the problem.

assume x = 5

f(x) = |5-38| = |-33| = 33

g(f(x)) is therefore equal to g(33) which is equal to -13*33 + 5 which is equal to -424.

if you set h(x) = (g o f)(x) = g(f(x)), then h(x) = -13 * |x-38| + 5

when x = 5, this becomes -13 * |5-38| + 5 which becomes -13 * 33 + 5 which becomes -424 which is the same as we got before.

i think your answer is that:

(g o f)(x) = g(f(x)) = -13 * |x-38| + 5

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!