# Precalculus : Inverse Functions

## Example Questions

### Example Question #31 : Inverse Functions

If , find

Explanation:

Set , thus .

Now switch  with .

So now,

.

Simplify to isolate  by itself.

So

Therefore,

.

Now substitute  with ,

so

, and

.

### Example Question #32 : Inverse Functions

Find the inverse of this function:

Explanation:

Write the equation in terms of x and y:

Switch the x and y (this inverts the relationship of the two variables):

Solve for y:

Rewrite to indicate this is the inverse:

### Example Question #1 : Inverses

Find  for

Explanation:

To find the inverse of a function, first swap the x and y in the given function.

Solve for y in this re-written form.

### Example Question #33 : Inverse Functions

Find the inverse of:

Explanation:

Interchange the variables and solve for .

Divide by four on both sides.

### Example Question #34 : Inverse Functions

Find the inverse function () of the function

None of these answers are correct.

Explanation:

f(x) can be called y. Switch x and y, and solve for y. The resulting new equation is the inverse of f(x).

To double check your work, substitute  into its inverse or vice versa. Both substitutions should equal x.

### Example Question #371 : Gre Subject Test: Math

Which of the following is the inverse of ?

Explanation:

Which of the following is the inverse of ?

To find the inverse of a function, we need to swap x and y, and then rearrange to solve for y. The inverse of a function is basically the function we get if we swap the x and y coordinates for every point on the original function.

So, to begin, we can replace the h(x) with y.

Next, swap x and y

Now, we need to get y all by itself; we can to begin by dividng the three over.

Now, recall that

And that we can rewrite any log as an exponent as follows:

So with that in mind, we can rearrange our function to get y by itself:

### Example Question #35 : Inverse Functions

Find the inverse function of this function: .

The inverse of this function is not a function.

Explanation:

Interchange the variables:

Solve for y:

Because f(x) passes the horizontal line test, its inverse must be a function.

### Example Question #36 : Inverse Functions

Find the inverse of the given function:

Explanation:

To find the inverse function, we want to switch the values for domain in range. In other words, switch out the  and  variables in the function:

### Example Question #37 : Inverse Functions

Find the inverse of the following function:

Explanation:

To find an inverse, simple switch f(x) and x and then solve for f(x). Thus, the inverse is:

### Example Question #38 : Inverse Functions

Find the inverse of the following function: