Question

Why isn't the inverse of a function always a function?

Answer 1

okay just suppose that you have a function lets say y= sin x
now inverse of it will be \[x= \sin^{-1}y\] so does the definition of function applies in inverse, try it ?

Answer 2

did you get it?

Answer 3

uhm no,

Answer 4

for defining a function it should have one output to the one input but when you will reverse the condition that is inverse , you will have same x for two Ys which contradicts the definition of function

Answer 5

and in some cases it is possible the inverse of a function could be a function like if i say y=f(x)=x its inverse could be a function but if i say y= x^3 its a function but inverse is not a function

Answer 6

still confused? @srw1496

Answer 7

uh yeah...

Answer 8

i am confused
if \(f(x)=x^3\) then \(f^{-1}(x)=\sqrt[3]{x}\) which is a function

Answer 9

@satellite73 i was missing you and i knew this

Answer 10

@srw1496 look fundamentally just check out the definition of function and if the inverse of function gives two values for same input then it is not a function

Answer 11

and yes my apology for choosing wrong example

Answer 12

on the other hand, lets look at \(f(x)=x^2\)
here we have \(f(2)=2^2=4\) and \(f(-2)=(-2)^2=4\) as well
so both \((-2,4)\) and \(2,4)\) are on the graph
but if you switch the ordered pairs, then you get both \((4,-2)\) and \((4,2)\) so the inverse is not a function

Answer 13

the difference is \(x^3\) is a "one to one" function, which means two different inputs give two different outputs
but \(x^2\) is not a one to one function, different inputs can give the same output

Answer 14

y=x^2 is not a function

Answer 15

q is not a letter

Answer 16

????!!!!

Answer 17

What are you talking about, seriously?

Answer 18

First you tell me arcsine isn't a function and now this? lol

Answer 19

this is not a pipe

Answer 20

yes plot y=x^2 and use straight line test , straight line cuts the parabola twice so its not a function

Answer 21

lets play

Answer 22

y=x^2 is a function. x=sqrt(y) is not for all y. Only positive y.

Answer 23

function @Kainui dad

Answer 24

LOL

Answer 25

uhhh i have no idea what is going on...

Answer 26

It's not injective. That doesn't mean it isn't a function...

Answer 27

we are having useless debate but @srw1496 i think @satellite73 has explained everything that is all you need to know

Answer 28

You cut yours the wrong way, kid. Study my picture carefully and you'll see.