IXL - Find the inverse of a rational function (Algebra 2 practice)

Find the inverse of the function.

(

)

–

Write your answer in the form

where

and

are integers.

–

(

)

ref_doc_title.

Learn with an example

question

Find the inverse of the function.

(

)

–

Write your answer in the form

where

and

are integers.

–

(

)

key idea

A relation is a set of ordered pairs

(

)

If a relation pairs each

-value

with exactly one

-value,

the relation is called a

function.

The inverse of a relation has the

and

-values

swapped. So, if

(

)

is an ordered pair of the relation, then

(

)

is an ordered pair of its inverse. If the inverse of a function

(

)

is also a

function,

then it is called the inverse function and is written

–

(

)

When it's not specified, the domain of a relation is the set of all possible

-values.

Sometimes a smaller domain will be specified.

solution

To find the inverse of the function

(

)

–

Substitute
y
for
g
(
x
)
.
Swap the
x
and
y
variables.
Solve for the new
y
variable.

Substitute

for

(

)

(

)

–

Swap the

and

variables.

–

Solve for the new

variable.

First, multiply both sides by the denominator and group the

-terms

on one side of the equation. Then, factor out

and divide to solve for

–

(

–

)

Multiply both sides by

–

Multiply both sides by

–

Subtract

from both sides

Subtract

from both sides

–

Add

to both sides

Add

to both sides

(

–

)

Factor out

Divide both sides by

–

Divide both sides by

–

So, the inverse is

–

Since the inverse relation is a rational function, it is indeed a function.

This means

–

(

)

–

Looking for more? Try this:

Lesson: Inverse functions

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B.4Rearrange multi-variable equations

Lesson: Inverse functions

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