SOLUTION: Please help me with this: The function f(x) = {{{x^3}}} + x is a one-to-one function, and thus its inverse {{{f^-1}}} is also a function. Find the equation of the tangent line whi

Question 1033081: Please help me with this:
The function f(x) = + x is a one-to-one function, and thus its inverse is also a function. Find the equation of the tangent line which can be drawn to the graph of at the point (2,1).
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If , then plugging in into the former would lead to

==>
==> after implicit differentiation
==> after factoring...
Now one particular point in the graph of is (2,1).
==>
==> , or
==> , which is also the slope of the tangent line.
==> the equation of the tangent line to at the point (2,1) is , or .

As what would other tutors would point out later, the derivative at a point on the graph of is equal to the reciprocal of the derivative of the function f(x) at the inverse point, on condition that f'(x) at the inverse point is NOT zero.
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