Umkehrfunktion von f(x)=sin(x)/(sin(x)+2)

Question

Ich suche die Umkehrfunktions von f(x) = sin(x) / (sin(x) + 2)

Answer 1

y = sin(x) / ( sin(x) + 2 )

y*(sin(x) + 2)  = sin(x)

y*sin(x)+2y = sin(x)

y*sin(x) - sin(x) = -2y

sin(x) * ( y-1) = - 2y

sin(x)  = - 2y / ( y-1)  = 2y / ( 1 -y )

x = arcsin ( 2y / (1- y) )

also f^{-1}(x)   =  arcsin (  2x / (1-x) )

Answer 2

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