SOLUTION: 1. a) Define a function: b) Define an inverse function: c) Given a function f(x), when does f^-1(x) exist?

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Question 1190839: 1.
a) Define a function:
b) Define an inverse function:
c) Given a function f(x), when does f^-1(x) exist?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a) Define a function:
A function is a relation for which each value from the set the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

b) Define an inverse function:
Inverse function is represented by f%5E-1%28x%29 with regards to the original function f+%28x%29and the domain of the original function becomes the range of inverse function and the range of the given function becomes the domain of the inverse function.

c) Given a function f%28x%29, when does f%5E-1%28x%29 exist?
For any inverse to exist, function has to be one-one onto, i. e. bijective.
The inverse exists when we can get back to an x given a y.