Question

Which equation is the inverse of y = 16x2 + 1?

Answer 1

Answer:

$y=\frac{\sqrt{x-1} }{4}$

Step-by-step explanation:

The given equation is

$y=16x^2+1$

For this function to have an inverse, we must restrict the domain, say $x\ge0$

We interchange x and y to get,

$x=16y^2+1$

We now make y the subject to get;

$x-1=16y^2$

$x-1=16y^2$

We divide through by 16 to get;

$\frac{x-1}{16}=y^2$

We now take the square root of both sides to get;

$\pm \sqrt{\frac{x-1}{16}}=y$

$y=\pm \frac{\sqrt{x-1} }{4}$

Since  $x\ge 0$, the inverse function is

$y=\frac{\sqrt{x-1} }{4}$