The number of real solutions #cos(e^x)=2^x + 2^-x# is ?

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Answer 1 · 2018-02-25T16:59:44

See below.

#2^x+2^-x# is an even function with minimum at #x = 0#

or #2 le 2^x+2^-x#

also we know that

#-1 le cos(y) le 1#

and the conclusion is that

#cos(y)# and #2^x+ 2^-x# does not intercept so no real solution is possible for

#cos(e^x)=2^x + 2^-x#