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Inverse of $$$y = 16 x^{2} + 1$$$
The calculator will try to find the inverse of the function $$$y = 16 x^{2} + 1$$$, with steps shown.
Related calculator: Inverse Function Calculator
Solution
To find the inverse function, swap $$$x$$$ and $$$y$$$, and solve the resulting equation for $$$y$$$.
This means that the inverse is the reflection of the function over the line $$$y = x$$$.
If the initial function is not one-to-one, then there will be more than one inverse.
So, swap the variables: $$$y = 16 x^{2} + 1$$$ becomes $$$x = 16 y^{2} + 1$$$.
Now, solve the equation $$$x = 16 y^{2} + 1$$$ for $$$y$$$.
$$$y = - 4 \sqrt{x - 1}$$$
$$$y = 4 \sqrt{x - 1}$$$