How to prove that #f# is continuous?
#f,g:R->R# with
#g(x)=f(f(x)) + e^x# ,#xεR#
supposed #f# , #g# are strictly increasing and for #x_0εR# , #lim_(xrarrx_0)f(x)=l#
supposed
1 Answer
Dec 5, 2017
Explanation:
- If
#x<# #x_0# #=># #x->x_0^-# #=># #f(x)# #<# #f(x_0)# , because#f# strictly increasing
so
- If
#x># #x_0# #=># #=># #x->x_0^+# #=># #f(x)# #># #f(x_0)# , because#f# strictly increasing
so
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