Find the Inverse of a Function - Pre-Calculus

First, switch the variables making into .

Then solve for y by taking the square root of both sides.

To find the inverse in this case, we need to switch our x and y variables and then solve for y.

Therefore,

becomes,

To solve for y we square both sides to get rid of the sqaure root.

We then subtract 2 from both sides and take the exponenetial of each side, leaving us with the final answer.

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable in the resulting equation.

Simplifying a number with 0 as the power, the inverse is

To find the inverse of y, or

first switch your variables x and y in the equation.

Second, solve for the variable in the resulting equation.

And by setting each side of the equation as powers of base e,

To find the inverse we need to switch the variables and then solve for y.

Switching the variables we get the following equation,

.

Now solve for y.

We begin by taking and changing the to a , giving us .

Next, we switch all of our and , giving us .

Finally, we solve for by subtracting from each side, multiplying each side by , and dividing each side by , leaving us with,

.

So we first replace every with an and every with a .

Our resulting equation is:

Now we simply solve for y.

Subtract 9 from both sides:

Now divide both sides by 10:

The inverse of

is

To find the inverse of a function we just switch the places of all and with eachother.

So

turns into

Now we solve for

Divide both sides by

To find the inverse, substitute all x's for y's and all y's for x's and then solve for y.

To find the inverse of the function, we switch the switch the and variables in the function.

Switching and gives

Then, solving for gives our answer:

To find the inverse of the function, we must swtich and variables in the function.

Switching and gives:

Solving for yields our final answer:

To find the inverse of the function, we can switch and in the function and solve for :

Switching and gives:

Solving for yields our final answer:

To find the inverse of the function, we can switch and in the function and solve for .

Switch and :

We can now solve for :

To find the inverse of the function, we simply need to switch the values of and and solve for .

Switching and , we can write the function as:

We now subtract to solve for :

To find the inverse of this function, we switch and in the function:

We now solve for :

To find the inverse of this function we can switch the and variables and solve for .

First, switch and in the function:

Now, solve for :

To find the inverse of the function, we switch and in the function.

We can now find our answer by solving for :

To find the inverse of the function, we swtich and in the function.

Solve for :

In order to have the inverse of a function, the new function must perform the inverse opperations in the opposite order. One way to ensure that is true is to consider the case of , switch x and y, then solve for y.

in this case becomes .

Our first step in solving is to take the reciprocal power on each side.

The reciprocal of 5 is , so we'll take both sides to the power of 0.2:

Now divide by 2:

Note that the answer has the correct inverse opperations, it is just in the wrong order - first you divide by 2, then you take x to the power of 0.2.