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

Question

asked Jan 5, 2023 216k views

1 Answer

CrimsonDark · Answer 1 · 2023-01-11T18:25:58+0000

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

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:

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

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.