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Hovedindhold

Aktuel tid:0:00Samlet varighed:2:17

This right over here is our understanding inverses of functions
exercise on Khan Academy. It's a good exercise to make sure
you understand inverses of functions. It's an interactive one
where we can move this line around and it tells us 'the graph of h(x)
is the green', so that's this dotted green line,
'the dashed line segment shown below'. So that's this. 'Drag the endpoints of the segment below
to graph h inverse of (x). There's a couple of ways to tackle it. Perhaps the simplest one
is we say, okay, look, h(x), what does h(x)
map from and to? So h(x), this point
shows that h(x), if you input -8 into h of (x),
h of -8 is 1, so it's mapping from -8 to 1. Well, the inverse of that, then,
should map from 1 to -8. So let's put that point on the graph,
and let's go on the other end. On the other end of h of x, we see that when you input 3 into h of x,
when x is equal to 3, h of x is equal to -4. So this point shows us
that it's mapping from 3 to -4. So the inverse of that would map
from -4 to 3. If you input -4 it should output 3. Since we took
the two end points of this line and found the inverse mapping of it, what I have just done here
is that I have graphed the inverse. Another way to think about the inverse is if you were to draw the line y = x, these things should be reflections
around the line y =x because one way to think about it is,
you're swapping the xs for the ys. If you were to draw the line y = x, if you flipped it around,
the line y = x, the green line, you would actually get the old line. This would flip over there
and this would flip over there. But either way, we're done.
We have graphed h inverse of x.