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Cartesian Product

Consider func...

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Consider functions f and g such that composite gof is defined and is one-one. Are f and g both necessarily one-one.

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Q. Consider functions f and g such that composite gof is defined and is one are g both necessarily one-one.

Q. If f : A → B and g : B → C are one-one functions, show that gof is a one-one function.

Q. Consider a differential function

f (x)

on the set of real numbers such that

f (- 1) = 0

| f^{'} (x) | \leq 2

. Given these conditions, which one of the following inequalties is necessarily ture for all

x ϵ [- 2, 2]

?

If functions $f : A \to B$ and $g : B \to A$ satisfy $g o f = I_{A}$ , then show that f is one-one and g is onto.

A = R - {3}

B = R - {1}

. consider the function

f : A

\to

B

f (x) = (\frac{x - 2}{x - 3})

. Show that f is one-one and onto and hence find

f^{- 1}

.

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