Question

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

Answer 1

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

Step-by-step explanation:

$y=2x^2+1$

We change the argument and the value:

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

Divide both parts of the equation by 2:

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

The restrictions are imposed on the inverse function by on x:

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

The restrictions are imposed on the inverse function by on y:

$y\geq 0$

Then the original function is defined on the sets:

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

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