(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[itex] f(x) = 3x^2-6 [/itex]

We are asked to solve for the inverse function of the above function.

2. Relevant equations

3. The attempt at a solution

[itex] y=3x^2-6 [/itex]

[itex] x=3y^2-6 [/itex]

[itex] \frac{3y^2=x+6}{3} [/itex]

[itex] y^2 = \frac{x+6}{3} [/itex]

[itex] \sqrt{y^2}= \frac{\sqrt{x+6}}{3} [/itex]

[itex] y= \frac{\sqrt{x+6}}{\sqrt{3}} [/itex]

[itex] y= \frac{\sqrt{x+6}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} [/itex]

[itex] y= \frac{\sqrt{3x+18}}{3} [/itex]

[itex] f^{-1}(x) = \frac{\sqrt{3x+18}}{3} [/itex]

however, my teacher marked me wrong. I don't know why. I might ask her tomorrow but it's our mastery test and she might not explain it to me. Anyone care to tell me what wrong I did? Is it the rationalization? Is it supposed to have a radical denominator? Thank!

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# Homework Help: Simplifying Inverse Functions

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