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EastWind [94]
3 years ago
11

What is the equation (simplified) the inverse of y=2x^2?

Mathematics
1 answer:
Yuki888 [10]3 years ago
3 0
2x^2=y\ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y}{2}\\\\\boxed{x=\sqrt{\frac{y}{2}}}\\\\x=\dfrac{\sqrt{y}}{\sqrt2}=\dfrac{\sqrt{y}\cdot\sqrt2}{\sqrt2\cdot\sqrt2}\to\boxed{x=\dfrac{\sqrt{2y}}{2}}\\\\\\\boxed{f(x)=2x^2\to f^{-1}(x)=\dfrac{\sqrt{2y}}{2}}
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Step-by-Step explanation:

Common knowledge: Anytime you have the same numerator, with a different denominator, the one with the bigger denominator is always smaller. For example, if had a pizza with 6 slices and a pizza with 4 slices, the one with 6 slices and smaller and the one with 4 slices and bigger. Even though 6>4 that mindset has to change when thinking about a problem like this.

<em>Another explanation: </em>

<em>If you still don’t get it, simply find a common denominator, so we’ll choose 12. Take 3/6 and multiply that by 2/2 so you get 6/12 and then take 3/4 and multiply that by 3/3 on both the (numerator and denominator) and that equals 9/12.</em>

<em>So now you have the expression: 6/12<9/12.</em>

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