Respuesta :

TaeKwonDoIsDead

Answer:

[tex]\sqrt{\frac{x}{4}}[/tex]  and  [tex]-\sqrt{\frac{x}{4}}[/tex]

Step-by-step explanation:

The function is given as  [tex]f(x)=4x^2[/tex]

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:

[tex]f(x)=4x^2\\y=4x^2\\x=4y^2\\y^2=\frac{x}{4}\\y=+-\sqrt{\frac{x}{4}}[/tex]

These 2 are the inverse functions.

carlosego

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

[tex]f (x) = 4x ^ 2[/tex]

We follow the steps below:

Replace f (x) with y:

[tex]y = 4x ^ 2[/tex]

We exchange variables;

[tex]x = 4y ^ 2[/tex]

We solve for y:

[tex]4y ^ 2 = x[/tex]

We divide between 4 on both sides of the equation:

[tex]y^ 2 = \frac {x} {4}[/tex]

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

[tex]y = \pm \sqrt {\frac {x} {4}}[/tex]

We substitute y for [tex]f ^ {- 1} (x)[/tex]:

 [tex]f ^ {- 1} (x) =\pm \sqrt {\frac {x} {4}}[/tex]

Answer:

[tex]f^{-1}(x)=\pm\frac{\sqrt{x}}{2}[/tex]

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