Calculate the function

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High School Math Grades 9-12, Ages 13-18

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High School Math Grades 9-12, Ages 13-18

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Calculate the function

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inverse function

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Arkham

#1 h Apr 29, 2021, 4:55 PM

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Consider $y = f (x) = \arcsin (- \sqrt {1 + 10x})$ , $x \in [-1 / 10,0]$ . Calculate the function where $g$ is the inverse function of $f$

Note: $g (y) = f ^ {- 1} (y)$ ]

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#2 h May 18, 2025, 9:03 AM

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Swapping $y$ with $x$ yields:

$x = \arcsin(-\sqrt{1+10y})$ ;

or $-\sin(x) = \sqrt{1+10y}$ (for $x \in [-\pi/2,0], y \in [-1/10,0]$ );

or $\sin^{2}(x) = 1+10y$ ;

or $y = -\frac{1-\sin^{2}(x)}{10}$ ;

or $\textcolor{red}{y =f^{-1}(x) = -\frac{\cos^{2}(x)}{10}}$ (for $x \in [-\pi/2,0]$ ).

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