Chapter 2: Q14E (page 115)
Question: Determine whether is onto if
Answer:
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a) Define the inverse of a function
b) When does a function have an inverse?
C) Does the function from the set of integers to the set of integers have an inverse? If so, what is it?
Show that the function from the set of real numbers to the set of non-negative real numbers is not invertible, but if the domain is restricted to the set of non- negative real numbers, the resulting function is invertible.
a) Prove that a strictly decreasing function from R to itself is one-to-one.
b) Give an example of a decreasing function from R to itself is not one-to-one.
Show that matrix multiplication is not commutative.
Question: a) Prove that a strictly increasing function from R to itself is one-to-one.
b) Give an example of an increasing function from R to itself is not one-to-one.
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