Question

Which is the inverse of the function f(x) = 4x2

Answer 1

`\sqrt{(x)/(4)}` and
`-\sqrt{(x)/(4)}`

Explanation:

The function is given as
`f(x)=4x^2`

to find inverse, we follow the steps shown below:

1. write "y" in place of "f(x)"

2. interchange "x" and "y"

3. solve for the new "y"

4. replace y with f^-1(x)

Let's do this:

`f(x)=4x^2\\y=4x^2\\x=4y^2\\y^2=(x)/(4)\\y=+-\sqrt{(x)/(4)}`

These 2 are the inverse functions.

Answer 2

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

`f (x) = 4x ^ 2`

We follow the steps below:

Replace f (x) with y:

`y = 4x ^ 2`

We exchange variables;

`x = 4y ^ 2`

We solve for y:

`4y ^ 2 = x`

We divide between 4 on both sides of the equation:

`y^ 2 = \frac {x} {4}`

We apply square root to both sides to eliminate the exponent:

`y = \pm \sqrt {\frac {x} {4}}`

We substitute y for
`f ^ {- 1} (x)`:

`f ^ {- 1} (x) =\pm \sqrt {\frac {x} {4}}`

Answer:

`f^(-1)(x)=\pm(√(x))/(2)`