Question

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

Answer 1

Answer:

$\sqrt{\frac{x}{4}}$  and  $-\sqrt{\frac{x}{4}}$

Step-by-step 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:

$f(x)=4x^2\\y=4x^2\\x=4y^2\\y^2=\frac{x}{4}\\y=+-\sqrt{\frac{x}{4}}$

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:

$f^{-1}(x)=\pm\frac{\sqrt{x}}{2}$