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