IXL - Inverse function rule (Calculus practice)

The function

has the inverse function

–

(

–

)

and

′

(

–

)

–

what is

(

–

)

′

(

)

ref_doc_title.

Learn with an example

question

The function

has the inverse function

–

(

–

)

–

and

′

(

–

)

what is

(

–

)

′

(

–

)

key idea

A function

has an inverse function if each output value of

comes from exactly one input value.

The inverse function of

is written

–

The function

–

takes each output value of

to the corresponding input value:

–

(

)

if and only if

(

)

(

)

and

′

(

)

≠

the derivative of

–

evaluated at

(

–

)

′

(

)

′

(

–

(

)

solution

Rewrite

(

–

)

′

(

–

)

using the formula for the derivative of an inverse function:

(

–

)

′

(

–

)

′

(

–

(

–

)

The denominator is a composition of functions. To find it, work inside out.

Start with

–

(

–

)

Since

(

–

)

–

you know that

–

(

–

)

–

Substitute this into the formula.

(

–

)

′

(

–

)

′

(

–

(

–

)

′

(

–

)

You know that

′

(

–

)

so complete the calculation.

(

–

)

′

(

–

)

′

(

–

)

So,

(

–

)

′

(

–

)

Looking for more? Try this:

$Confetti$

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Work it out

Not feeling ready yet? This can help:

B.2Find values of inverse functions from tables

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