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Functionby thereddevils
Tags: function 
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#1
May1910, 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 ? 


#2
May1910, 06:39 AM

P: 2,179

This looks correct to me.



#3
May1910, 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.



#4
May1910, 07:00 AM

P: 439

Function



#5
May1910, 07:10 AM

Mentor
P: 15,067

Show your steps on how you derived g(f(x)).



#6
May1910, 07:30 AM

P: 439




#7
May1910, 07:35 AM

Mentor
P: 15,067

Hint: Is f(x) ever negative?



#8
May1910, 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?



#9
May1910, 07:47 AM

P: 439




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