MATH SOLVE

2 months ago

Q:
# Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}

Accepted Solution

A:

an expression, that is a function, will have no x-repeats on the x,y pairs.

and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then,

[tex]\bf a \qquad\{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)\}\\\\ b \qquad\{(-1, 2), (0, \stackrel{\downarrow }{4}), (1, 5), (5, \stackrel{\downarrow }{4}), (7, 2)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]

[tex]\bf c \qquad\{(-1, -2), (0, \stackrel{\downarrow }{4}), (1, 3), (5, 14), (7, \stackrel{\downarrow }{4})\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}\\\\ d \qquad\{(-1, \stackrel{\downarrow }{4}), (0, \stackrel{\downarrow }{4}), (1, 2), (5, 3), (7, 1)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]

and expression that is a function, and has an inverse that is also a function, will have no x-repeats, and no y-repeats either, so the pairs will be unique for the set, let's do some checking then,

[tex]\bf a \qquad\{(-1, 3), (0, 4), (1, 14), (5, 6), (7, 2)\}\\\\ b \qquad\{(-1, 2), (0, \stackrel{\downarrow }{4}), (1, 5), (5, \stackrel{\downarrow }{4}), (7, 2)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]

[tex]\bf c \qquad\{(-1, -2), (0, \stackrel{\downarrow }{4}), (1, 3), (5, 14), (7, \stackrel{\downarrow }{4})\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}\\\\ d \qquad\{(-1, \stackrel{\downarrow }{4}), (0, \stackrel{\downarrow }{4}), (1, 2), (5, 3), (7, 1)\}\impliedby \begin{array}{llll} \textit{notice the } y-rep eats\\ \textit{thus, no dice} \end{array}[/tex]