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Function

by thereddevils
Tags: function
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thereddevils
#1
May19-10, 04:44 AM
P: 439
1. The problem statement, all variables and given/known data

Function f and g are defined as follows :

f(R)=R , f(x)=x^2 , g(R)=R , g(x)=x+1,x>=0 , -x , x<0 (its a piecewise function) . Find fg(x) and gf(x) .

2. Relevant equations



3. The attempt at a solution

fg(x)=
(x+1)^2 , x>=0
x^2 , x<0

gf(x)=
x^2+1 , x>=0
-x^2 , x<0

Am i correct ? What are the things i will need to look into when face questions like this ? Cheking the domain ?
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phyzguy
#2
May19-10, 06:39 AM
P: 2,179
This looks correct to me.
D H
#3
May19-10, 06:54 AM
Mentor
P: 15,067
If you mean f(g(x)) and g(f(x)) then what you have for f(g(x)) is correct, but the other is not.

thereddevils
#4
May19-10, 07:00 AM
P: 439
Function

Quote Quote by D H View Post
If you mean f(g(x)) and g(f(x)) then what you have for f(g(x)) is correct, but the other is not.
thanks but why ? How did you see that ?
D H
#5
May19-10, 07:10 AM
Mentor
P: 15,067
Show your steps on how you derived g(f(x)).
thereddevils
#6
May19-10, 07:30 AM
P: 439
Quote Quote by D H View Post
Show your steps on how you derived g(f(x)).
ok . Basically , i just substituted the function f(x) into the function g(x) , without doing any other checkings because i do not know what to check . Could you guide me on thsi ? Thanks .
D H
#7
May19-10, 07:35 AM
Mentor
P: 15,067
Hint: Is f(x) ever negative?
phyzguy
#8
May19-10, 07:40 AM
P: 2,179
Ah, based on DH's hint, I now agree that you have done g(f(x)) incorrectly. Thereddevils, do you see it now?
thereddevils
#9
May19-10, 07:47 AM
P: 439
Quote Quote by D H View Post
Hint: Is f(x) ever negative?
thanks !


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