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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 $Y$,
   $f^{-1}(C) =$ _____.

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