IXL - Check whether two rational functions are inverses (Precalculus practice)

Are

(

)

and

(

)

inverse functions on the set of

-values

where their compositions are defined?

(

)

–

(

)

–

yes

ref_doc_title.

Learn with an example

question

Are

(

)

and

(

)

inverse functions on the set of

-values

where their compositions are defined?

(

)

–

(

)

yes

key idea

(

)

and

(

)

are inverse functions on the set of

-values

where their compositions are defined if and only if the following equations are true:

(

∘

)

(

)

(

)

(

∘

)

(

)

(

)

To find

(

∘

)

(

)

(

∘

)

(

)

use the inner function as the input for the outer function. The inverse of

(

)

is written

–

(

)

solution

Find

(

∘

)

(

)

(

∘

)

(

)

(

)

Substitute the inner function,

(

)

Substitute the inner function,

(

)

Apply the function rule for the outer function,

(

)

–

Apply the function rule for the outer function,

(

)

–

Multiply the constants by

(

)

to get a common denominator.

–

Multiply the constants by

to get a common denominator.

–

(

)

(

)

–

To divide, multiply by the reciprocal

–

To divide, multiply by the reciprocal

–

Since

(

∘

)

(

)

≠

and

are not inverse functions and the answer is

no.

Looking for more? Try these:

Lesson: Inverse functions

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Not feeling ready yet? These can help:

B.1Identify inverse functions

X.6Add and subtract rational expressions

X.5Multiply and divide rational expressions

Lesson: Inverse functions

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