Example 1: Find the inverse function of f given by
f(x) = 2x + 3
Solution to example 1:
 write the function as an equation.
 solve for x.
 now write f^{1}(y) as follows .
or f^{ 1}(x) = (x  3)/2

Check
 f(f^{ 1}(x))=2(f^{ 1}(x)) + 3
=2((x3)/2)+3
=(x3)+3
=x
 f^{ 1}(f(x))=f^{ 1}(2x+3)
conclusion: The inverse of function f given above is
f^{ 1}(x) = (x  3)/2
Matched Exercise 1: Find the inverse function of f given by
f(x) = x  4
Example 2: Find the inverse function of f given by
f(x) = (x  3)^{2}, if x >= 3
Solution to example 2:
 write the function as an equation.
 solve for x, two solutions .
 the first solution is selected
since x >= 3, write f^{1}(y) as follows.
 Check
f(f^{ 1}(x))=((3+sqrt(x))3)^{2}
f^{ 1}(f(x))=3+sqrt((x3)^{2})
=3+x3 (since x >= 3, x3 >= 0, x3 = x3)
conclusion:
The inverse of function f given above is
f^{ 1}(x) = 3 + sqrt(x)
Matched Exercise 2: Find the inverse function of f given by
f(x) = (x + 1)^{2}, if x >= 1
Example 3: Find the inverse function of f given by
f(x) = (x + 1)/(x  2)
Solution to example 3:
 Write the function as an equation.
 Multiply both sides of the above equation by x  2 and simplify.
 Multiply and group.
 Factor x on the left side and solve
 Change x to y and y to x
y = (1 + 2x) / (x  1)
 The inverse of function f given above is
f^{ 1}(x) = (1 + 2x) / (x  1)
Matched Exercise 3: Find the inverse function of f given by
f(x) = (x + 1)/(x  1
Answers to the Matched Exercises
Answer to Matched Exercise 1
f^{ 1}(x) = x  4
Answer to Matched Exercise 2
f^{ 1}(x) = 1 + sqrt(x)
Answer to Matched Exercise 3
f^{ 1}(x) = (x + 1)/(x  1)
More links and references related to the inverse functions.
Find the Inverse Functions  Calculator
Applications and Use of the Inverse Functions
Find the Inverse Function  Questions
Inverse of Quadratic Functions.
Definition of the Inverse Function  Interactive Tutorial
Find Inverse Of Cube Root Functions.
Find Inverse Of Square Root Functions.
Find Inverse Of Logarithmic Functions.
Find Inverse Of Exponential Functions.
