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## Precalculus

### Course: Precalculus > Unit 1

Lesson 4: Inverse functions in graphs and tables# Reading inverse values from a table

An inverse function takes the output from the original function and gives us the input. Given a table of inputs and outputs for a function, evaluate the inverse function for a certain input. Created by Sal Khan.

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## Video transcript

- [Instructor] We're
told the following table shows a few inputs and outputs
of function G, all right. We have some possible inputs here for X and then the corresponding
outputs here, G of X. What is the value of G inverse of 54? So pause this video and see
if you can figure that out before we work through it together. All right. Let's just remind ourselves what an inverse function even does. So if you have some
value, X and you input it into some function, G, that function is going to output G of X. And an inverse function
takes us the other way. We could take this what was the output of G, G of X. We can input that into
an inverse function. The inverse function of G and that is actually going to give us X. It's going to get us back
to our original input right over here. So what we're focused on right
over here is G inverse of 54. So we can think about this part of this little chain that we set up. So what we're inputting into
this inverse function is 54. So what we want to say is, all right, when G of X is equal to 54, what is X? And we can see that right over here. When G of X is 54, the
corresponding input, original input, one way to think about it, is 62. So this will be equal to 62. Now some of you might have been
tempted to say, okay, look. It looks like I'm inputting
a 54 into a function. So I'll say, okay, X is the input. Let me just go to 54 right
over there as the input. But remember, this 54 isn't an
input into the inverse of G. This is an input into G of X. So if you wanted to evaluate this, if you wanted to evaluate G of 54, then you would look at the
54 up here and say, okay, that's going to be equal to 65. But we're looking at the inverse of G. So one way to think about it
is when 54 is the output in G, what is going to be the input? And we see that that is 62.