Register to reply 
Continuous and differentiable function 
Share this thread: 
#1
Feb1312, 06:05 PM

P: 19

1. The problem statement, all variables and given/known data
function f:R>R can be written as a sum f=f1+f2 where f1 is even and f2 is odd。show that if f is continuous then f1 and f2 may be chosen continuous, and if f is differentiable then f1 and f2 can be chosen differentiable 2. The attempt at a solution i have try some examples, but i still cannot get the idea from that 


#2
Feb1312, 06:10 PM

Sci Advisor
HW Helper
Thanks
P: 25,228




#3
Feb1312, 06:10 PM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,568

Given function f, let [itex]f_e(x)= (f(x)+ f(x))/2[/itex] and [itex]f_o(x)= (f(x) f(x))/2[/itex].



#4
Feb1312, 06:15 PM

P: 19

Continuous and differentiable function



#5
Feb1312, 06:20 PM

Sci Advisor
HW Helper
Thanks
P: 25,228




#6
Feb1312, 06:36 PM

P: 19




#7
Feb1312, 07:32 PM

Sci Advisor
HW Helper
Thanks
P: 25,228




Register to reply 
Related Discussions  
Inflection point of non continuous or non differentiable function  Calculus & Beyond Homework  3  
Analysis help  Continuous function that is differentiable at all points except c  Calculus & Beyond Homework  4  
Show a function is differentiable everywhere, and show its derivative is continuous  Calculus & Beyond Homework  1  
Continuous and differentiable Of Cos  Calculus & Beyond Homework  1 