What is the inverse of #f(x) = 3^(x^2-3x)# ?

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Answer 1 · 2015-11-24T03:34:16

#y=3/2+-sqrt(log_3x+9/4)#

#y=3^(x^2-3x)#

Flip #x# and #y#.

#x=3^(y^2-3y)#

Solve for #y#.

#log_3x=log_3(3^(y^2-3y))#

#log_3x=y^2-3y#

#log_3x+9/4=y^2-3y+9/4#

#log_3x+9/4=(y-3/2)^2#

#+-sqrt(log_3x+9/4)=y-3/2#

#y=3/2+-sqrt(log_3x+9/4)#