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🚧 Fin 7.1

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1. Given a function $f$ from a set $X$ to a set $Y$, $f(x)$ is _____. 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 2. Given a function $f$ from a set $X$ to a set $Y$, if $f(x) = y$ then $y$ is
called _____ or _____ or _____. 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 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 _____. 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 4. Given a function $f$ from a set $X$ to $Y$, if $f(x) = y$ then $x$ is called
_____ or _____. _____ 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 5. Given a function $f$ from a set $X$ to a set $Y$, if $y \in Y$ then
$f^{-1}(y) =$ _____ and is called _____. $f^{-1}(y) =$ _____ 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 6. Given functions $f$ and $g$ from a set $X$ to a set $Y$, $f = g$ if, and only
if, _____. if, _____.
$f(x) = g(x)$ for every $x \in X$
7. Given positive real numbers $x$ and $b$ with $b \neq 1$, $\log_b(x) =$ _____. 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 $X$, 8. Given a function $f$ from a set $X$ to a set $Y$ and a subset $A$ of $X$,
$f(A) =$ _____. $f(A) =$ _____.
$\{y \in Y | y = f(x) \text{ for some } x \in A\}$
9. Given a function $f$ from a set $X$ to a set $Y$ and a subset $C$ of $Y$, 9. Given a function $f$ from a set $X$ to a set $Y$ and a subset $C$ of $Y$,
$f^{-1}(C) =$ _____. $f^{-1}(C) =$ _____.
$\{x \in X | f(x) \in C\}$