47 lines
1.4 KiB
Markdown
47 lines
1.4 KiB
Markdown
Page 458
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**Test Yourself**
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1. Given a function $f$ from a set $X$ to a set $Y$, $f(x)$ is _____.
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the unique output element in $Y$ that is related to $x$ by $f$.
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2. Given a function $f$ from a set $X$ to a set $Y$, if $f(x) = y$ then $y$ is
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called _____ or _____ or _____.
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the value of $f$ at $x$; the image of $x$ under $f$; the output of $f$ for the
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input $x$
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3. Given a function $f$ from a set $X$ to a set $Y$, the range of $f$ (or the
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image of $X$ under $f$) is _____.
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the set of all $y$ in $Y$ such that $f(x) = y$
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4. Given a function $f$ from a set $X$ to $Y$, if $f(x) = y$ then $x$ is called
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_____ or _____.
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an inverse image of $y$ under $f$; a preimage of $y$
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5. Given a function $f$ from a set $X$ to a set $Y$, if $y \in Y$ then
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$f^{-1}(y) =$ _____ and is called _____.
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$\{x \in X | f(x) = y\}$; the inverse image of $y$
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6. Given functions $f$ and $g$ from a set $X$ to a set $Y$, $f = g$ if, and only
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if, _____.
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$f(x) = g(x)$ for every $x \in X$
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7. Given positive real numbers $x$ and $b$ with $b \neq 1$, $\log_b(x) =$ _____.
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the exponent to which $b$ must be raised to obtain $x$.
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8. Given a function $f$ from a set $X$ to a set $Y$ and a subset $A$ of $X$,
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$f(A) =$ _____.
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$\{y \in Y | y = f(x) \text{ for some } x \in A\}$
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9. Given a function $f$ from a set $X$ to a set $Y$ and a subset $C$ of $Y$,
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$f^{-1}(C) =$ _____.
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$\{x \in X | f(x) \in C\}$
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