F(z)=1/z

Solution for F(z)=1/z equation:

(F)=1/F

We move all terms to the left:

(F)-(1/F)=0


Domain of the equation: F)!=0

F!=0/1

F!=0

F∈R


We add all the numbers together, and all the variables

F-(+1/F)=0

We get rid of parentheses

F-1/F=0

We multiply all the terms by the denominator


F*F-1=0

Wy multiply elements

F^2-1=0

a = 1; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*1}=\frac{-2}{2}
=-1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*1}=\frac{2}{2}
=1
$