If f(u)=1+u+u²/u, prove that f(u)=f(1/u)?

Answer 1

f(1/u) = ( 1 + 1/u + 1/u^2 ) / (1/u)
= ( 1 + 1/u + 1/u^2 ) * u
= ( u + 1 + 1/u)
= ( 1 + u + u^2) / u
= f(u)

Answer 2

we can easily solve the equation

f(u) = 1+u+( u ^ 2 / u )

by the following method.

f(u)=1+u+u;
=1+2*u. ...................................... ( 1 )

f(1/u)=1/(1+u+u)
=1/(1+2*u) ...................................... ( 2 )

In order to prove that f(u)=f(1/u)

We must equalize both the equatio ( 1 ) and ( 2 )

(1+2*u) = 1/(1+2*u)
(1+2*u)*(1+2*u)=1
1+2*u+2*u+4*u^2=1
it will give

u= 0 , -1

when u=0

f(u)=1 and f(1/u)=1

when u= -1

f(u)= -1 and f(1/u)= -1

so it's prove that

f(u) = f(1/u) for any of the above value of ' U '

Answer 3

Please note that 1 + u + u² / u is not the same
as (1 + u + u²) / u
Assume you mean the latter.
f(u) = (1 + u + u²) / u
f(u) = 1/u + 1 + u
f(1/u) = 1/(1/u) + 1 + 1/u
f(1/u) = u + 1 + 1/u
Thus f(u) = f(1/u)

Answer 4

f(u)=1+u+u²/u
= 1/u +u/u + u²/u
= 1/u + 1 +u
= u+1/u +1
U can figure it out from here