Question

Find the inverse of the following function.

Answer 1

For this case we must find the inverse of the following function:

$f (x) = 8 \sqrt {x}$

For this, we follow the steps below:

We change f (x) to y:

$y = 8 \sqrt {x}$

We exchange the variables:

$x = 8 \sqrt {y}$

We solve for y:

$8 \sqrt {y} = x$

We divide between 8 on both sides of the equation:

$\sqrt {y} = \frac {x} {8}$

We raise both sides of the equation to the square to remove the root:

$y = (\frac {x} {8}) ^ 2\\y = \frac {x ^ 2} {64}$

So, the inverse is:$f ^ {- 1} (x) = \frac {x ^ 2} {64}$

ANswer:

Option C