Calculate #f (2)#, knowing that with any #x ≠ 0# the correct equality #f (x) + 3f (1 / x) = x ^ 2# ?

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Answer 1 · 2017-09-20T11:28:55

#-13/32#

Solve the system:

#f(2)+3f(1/2)=4#
#f(1/2)+3f(2) = 1/4#

for #f(2)#.

Or solve

#f(x)+3f(1/x)=x^2#
#f(1/x)+3f(x) = 1/x^2#

for #f(x) = - (x^4-3)/(8x^2)#

then evaluate at #x=2#.