Problem :
Find the inverse of f (x) = .
y = 

Solve for
x first:
(x  1)y   = x + 2 

xy  y   = x + 2 

xy  x   = y + 2 

x   = 

Now switch the variables
x and
y:
y = 

Problem :
Find the inverse of f (x) = 6 + 5x^{3}.
y   = 6 + 5x^{3} 

x   = 

Now switch variables:
y = 

Problem :
If f (3) = 2 and f'(3) = 7, what is (f^{1})'(2)?
(f^{1})(2) = , since the slope of the inverse is the
reciprocal.
Problem :
Find (f^{1})'(2) for f (x) = 4x^{3}  2x + 2.
Note that
f is not onetoone throughout its domain, so it does not have an inverse defined on its entire range.
However, there is a unique
x, namely 0, such that
f (x) = 2. So, for a suitable domain containing 0, the inverse
can be defined, and we may compute:
Problem :
Find (f^{1})'( 4) for f (x) = x^{3}  x^{2}  4x.
This problem doesn't make much sense, since there are several
x's such that
f (x) =  4. Namely,
they are
x =  2,
1, or
2.