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

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

We follow the steps below:

Replace f (x) with y:

We exchange variables;

We solve for y:

We divide between 4 on both sides of the equation:

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

We substitute y for :

 and  

Step-by-step explanation:

The function is given as  

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:

These 2 are the inverse functions.

The answer is option 1.

Step-by-step explanation:

First, you have to find the value of y. In order to find y, you have to use the area of rectangle as the question has given the area's value and the expressions for length and width :

Let area be 84 cm²,

Let length be (y+5) cm,

Let width be y cm,

Area = length×width

84 = y(y+5)

84 = y² + 5y

Next, you have to solve this equation by factorization :

y² + 5y = 84

y² + 5y - 84 = 0

y² + 12y - 7y - 84 = 0

y(y+12) - 7(y+12) = 0

(y-7)(y+12) = 0

y - 7 = 0

y = 7 cm

y + 12 = 0

y = -12 cm (rejected)

Lastly, you have to find the perimeter of rectangle using the formula, P = 2l + 2w where l represents length and w is width.

P = 2(y+5) + 2(y)

Let y = 7 cm,

P = 2(7+5) + 2(7)

= 2(12) + 14

= 24 + 14

= 38 cm