Question

Find the inverse. Determine whether the inverse represents a function.{(6, -10), (5, -9), (3, -8), (1, -7)}a{(-10, 6), (-9, 5), (-8, 3), (-7, 1)}; a functionb{(-10, 6), (-9, 5), (-8, 3), (-7, 1)}; not a functionc{(-9, -10), (-10, 3), (6, 5), (-9, -8)}; not a functiond{(-9, -10), (-7, 3), (6, 3), (-9, -8)}; a function

Answer 1

Given:

$\mleft\lbrace(6,-10\mright),(5,-9),(3,-8),(1,-7)\}$

For any function :

$y=f(x)$

Then inverse of function is:

$f^{-1}(y)=x$

so the any input and output of the function is exchange each other that mean any input function give output and use this output for inverse function as a input so given output is convert as a input for inverse function.

$\begin{gathered} \mleft\lbrace(6,-10\mright),(5,-9),(3,-8),(1,7)\} \\ is\text{ change as a} \\ \mleft\lbrace(-10,6\mright),(-9,5),(-8,3),(-7,1)\} \end{gathered}$

And is work as a inverse function.