Suppose f(x) is even function. if f(x) is continous at a, show f(x) continuous at -a ?

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Jim S Share
Mar 9, 2018

Answer:

Check below for detailed solution

Explanation:

  • #f# even means: for each #x##in##RR# , #-x##in##RR#

#f(-x)=f(x)#

  • #f# continuous at #x_0=a# #<=># #lim_(x->a)f(x)=f(a)#

#lim_(x->-a)f(x)#

Set #y=-x#
#x->-a#
#y->a#

#=# #lim_(y->a)f(-y)=lim_(y->a)f(y)=lim_(x->a)f(x)=f(a)#

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Sam F. Share
Feb 24, 2018

Answer:

See below

Explanation:

I'm not 100% sure about this, but this would be my answer.

The definition of an even function is #f(-x)=f(x)#

Therefore, #f(-a)=f(a)#. Since #f(a)# is continuous and #f(-a)=f(a)#, then #f(-a)# is also continuous.

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