Find the inverse of the given function.

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

We follow the steps below:

Replace f(x) with y:

We exchange the variables:

We solve for "y":

Multiply by -2 on both sides of the equation:

We raise both sides of the equation to the square to eliminate the radical:

We subtract 3 from both sides of the equation:

We change y by f ^ {- 1} (x):

.

Step-by-step explanation:

Given : .

To find : Find the inverse of the given function.

Solution : We have given

.

Step 1: take f(x) = y

.

Step 2 : Inter change y and x.

.

Step 3 : Solve for y

Taking square both sides

.

On multiply both sides by 4.

.

On subtraction both sides by 3.

.

Here, is inverse of f(x)

.

Therefore, .

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph