IXL - Identify inverse functions (Precalculus practice)

(

)

the inverse function of

(

)

(

)

(

)

–

yes

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Learn with an example

question

(

)

the inverse function of

(

)

(

)

(

)

–

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,

(

)

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,

(

)

–

Since

(

∘

)

(

)

(

∘

)

(

)

and

are inverse functions and the answer is

yes.

Looking for more? Try these:

Lesson: Inverse functions

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A.8Composition of functions

Lesson: Inverse functions

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