SOLUTION: Please help me with this problem: Suppose {{{f(x) = x^3}}} + 2x and {{{f^-1}}} is the inverse of {{{f}}}. Evaluate {{{f^-1(3)}}} and {{{(f^-1)}}}'{{{(3)}}}.

Question 1034949: Please help me with this problem:
Suppose + 2x and is the inverse of . Evaluate and '.
Found 2 solutions by solver91311, robertb:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I assume you are asking for both the inverse function and the first derivative of the inverse function.

Let

then

then

which is to say:

Swap the variables:

then

The latter being more convenient for using the power rule to find the first derivative.

Plug in the value 3 for x in each case.

John

My calculator said it, I believe it, that settles it

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
==> after plugging in the inverse into the original equation.
Now differentiate implicitly wrt x.
==>
Now ==> for all real x hence f(x) increasing ==> f(x) is one-to- DISABLED_event_one= => f(x) has an inverse function. Incidentally, f(1) = 3, and so .

==>
==>
Therefore,
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