What is the inverse of #y=xln( 3)+x^2?# ?

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Answer 1 · 2015-11-01T09:47:02

Choose + or -.

#y = f(x) \Rightarrow x = f^(-1)(y)#

Exchange x and y.

#x=yln(3)+y^2 \Rightarrow y = f^(-1)(x)#

So, we want y, but it is a parabola.

#y^2 + ln3 \cdot y - x = 0#

#Delta = (ln 3)^2 + 4x#

#y = f^-1(x) = \frac{- ln 3 ± sqrt Delta}{2}#