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 $y$ .

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

$log_3x=y^2-3y$

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

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

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

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

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