discrete_mathematics_with_applications/chapter_7/test_yourself.md

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Test Yourself

1. Given a function f from a set X to a set Y, f(x) is _____.

the unique output element in Y that is related to x by f.

2. Given a function f from a set X to a set Y, if f(x) = y then y is called _____ or _____ or _____.

the value of f at x; the image of x under f; the output of f for the input x

3. Given a function f from a set X to a set Y, the range of f (or the image of X under f) is _____.

the set of all y in Y such that f(x) = y

4. Given a function f from a set X to Y, if f(x) = y then x is called _____ or _____.

an inverse image of y under f; a preimage of y

5. Given a function f from a set X to a set Y, if y \in Y then f^{-1}(y) = _____ and is called _____.

\{x \in X | f(x) = y\}; the inverse image of y

6. Given functions f and g from a set X to a set Y, f = g if, and only if, _____.

f(x) = g(x) for every x \in X

7. Given positive real numbers x and b with b \neq 1, \log_b(x) = _____.

the exponent to which b must be raised to obtain x.

8. Given a function f from a set X to a set Y and a subset A of X, f(A) = _____.

\{y \in Y | y = f(x) \text{ for some } x \in A\}

9. Given a function f from a set X to a set Y and a subset C of Y, f^{-1}(C) = _____.

\{x \in X | f(x) \in C\}