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# Determining if a function is invertible

CCSS.Math:

## Video transcript

F is a finite function whose domain is the letters A to E the following table lists the output for each input and F's domain so if X is equal to a then so if we input a into our function then we output negative six f of a is negative six we input B we get three we input C we get negative 6 we input D we get two we input Y we get negative six build the mapping diagram for F by dragging the endpoints of the segments in the graph below so that they pair each domain element with its correct range element then determine if f is invertible all right so let's see what's going on over here let me scroll down a little bit more so in this purple oval this is representing the domain of our function f and this is the range so the function is going to if you give it a member of the domain it's going to map from that member of domain to a member of the range so for example you input a into the function it goes to negative six so a goes to negative six so I drag that right over there B goes to three B goes to three C goes to negative six so it's already interesting that we have multiple values that point to negative six so this is OK for F to be a function but we'll see it might make it a little bit tricky for F to be invertible so let's see d is points to two or maps to 2 so you input D into our function you're going to output 2 and then finally e maps to negative 6 as well a maps to negative 6 as well so that's a visualization of how this function f maps from a through e to members of the range but also ask ourselves is this function invertible and i already hinted at it a little bit well in order for it to be invertible you need a you need a function that could take go from each of these points to that can do the inverse mapping but it has to be a function so if you input 3 into this inverse function it should give you B if you input 2 into this inverse function it should output D if you input negative 6 into this into this inverse function well hypothetical inverse function what should it do well you can't have a function that if you input one if you input a number it could have three possible values a C or E you can only map to one value so there isn't you actually can't set up an inverse function that does this because it wouldn't be a function you can't go from input negative six into that inverse function and get three different values so this is not invertible let's do another example so here so this is same drill we have our members of our domain members of our range we can build our mapping diagram a maps to negative 36 B maps to 9 C maps to negative 4 D maps to 49 and then finally e map to 25 e maps to 25 now is this function invertible well let's think about it the inverse whoops the was a d maps to 49 a so let's think about what the inverse this hypothetical inverse function would have to do it would have to take each of these members of the range and do the inverse mapping so if we input 49 into our inverse function it should give you d input 25 you should give you e input 9 it gives you B you input negative 4 and then put C you input negative 36 it gives you a so you can easily construct an inverse function here so this is very much this is very much invertible one way to think about it is these are a this is this is a one-to-one mapping each of each of the members of the domain correspond to a unique member of the range you don't have two members of the domain pointing to the same member of the range anyway hopefully you found that interesting