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bixtya [17]
1 year ago
10

Find the Inverse Function : Algebra 2y = 2x² + 1​

Mathematics
1 answer:
Vera_Pavlovna [14]1 year ago
3 0

\displaystyle\\Answer:\ y=\sqrt{\frac{x-1}{2} }  \ \ \ \ (x\geq 1,\ \ \ \ y\geq 0)

Step-by-step explanation:

y=2x^2+1\\

<em>We change the argument and the value:</em>

\displaystyle\\x=2y^2+1\\\\x-1=2y^2+1-1\\\\x-1=2y^2\\

<em>Divide both parts of the equation by 2:</em>

\displaystyle\\\frac{x-1}{2}=y^2\\\\ \sqrt{\frac{x-1}{2} }=y \  -\  the\  desired\  inverse\  function\\\\

<em>The restrictions are imposed on the inverse function by on x:</em>

x-1\geq 0\\x\geq 1

<em>The restrictions are imposed on the inverse function by on y:</em>

y\geq 0

<em>Then the original function is defined on the sets:</em>

x\geq 1,\ \ \ \ y\geq 0

<em>The initial function, a parabola, is constrained because of the inverse function; only in this case the functions are reciprocal.</em>

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