Question

Find the inverse of this function defined by the given table

Answer 1

x: -2, -3, 6, 7 ,5.
y: 4, 2 , 1 ,3 , 4

Answer 2

if (x,y) is an element of f
then (y,x) is an element of the inverse of f

Answer 3

so example if (-2,4) is an element of f
then (4,-2) is an element of the inverse of f

Answer 4

also i assume you aren't looking for an inverse function
because no such function exist in this case
an inverse relation does exist though

Answer 5

so
x: 4 , 2 , 1 , 3 , 4
y: -2, -3 , 6, 7 , 5

Answer 6

yep
that is the inverse relation given of the function given

Answer 7

it asks if the inverse is a function

Answer 8

He told you:)

Answer 9

lol I didn't mean to pre answer any questions

Answer 10

hehe I wasn't knocking you;)

Answer 11

the reason it was not going to be an inverse function was because the function you submiited wasn't one to one
which means there will be a value in the inverse relation such that \[f^{-1}(value) \text{ will give you two outputs }\]

Answer 12

I'm talking about that value being 4

Answer 13

\[f^{-1}(x) \text{ should give us one value for } f^{-1} \text{ \to be noticed as a function } \\ \text{ but } f^{-1}(4)=-2 \text{ and } 5\]

Answer 14

i understand

Answer 15

notice for a relation to be a function one thing that must be true is that the relation is well defined, i.e. if x=y we have that f(x) = f(y). So when we are trying to see if a function has an inverse relation that is a function, we must make sure that our original function is one-to-one. i.e. if f(x) = f(y) then x=y. If a function is one-to-one, then its inverse relation will be well defined. Can you see how these are the same thing if we simply swap the x's with the y's?