g ( x ) = c * a^x
( x | y )
(2|1)
(4|4)
g ( 2 ) = c * a^2 = 1
g ( 4 ) = c * a ^4 = 4
c * a ^4 = 4
c * a ^2 = 1 | teilen, bei c / c = 1 entfällt
-----------------------
a^4 / a^2 = 4 / 1
a^2 = 4
a = + 2
und
a = - 2
Einsetzen + 2
c * a ^2 = 1
c * 2 ^2 = 1
c * 4 = 1
c = 1/4
Probe
c * a ^4 = 4
c * 2 ^4 = 4
1/4 * 2 ^4 = 4
1/4 * 16 = 4 Bingo
Einsetzen - 2
c * (-2) ^2 = 1
c = 1/4 dasselbe
g ( x ) = 1/4 * (+2) ^x
g ( x ) = 1/4 * (-2) ^x