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Bogdan [553]
3 years ago
6

Khan Academy

Mathematics
1 answer:
zvonat [6]3 years ago
7 0

Part 1

Answer: -9

---------------------------

Explanation:

Let's focus on evaluating   first. We need to look at the table and locate f(x) = 13. So we're looking in the f(x) row where 13 shows up. That's in the second to last column. Right above that we have x = 5

This means f(5) = 13 and   The inverse undoes the f(x) function. So the input x and output y values swap places. This is why we're reading the table in reverse.

<em>We can replace all of </em>f^{-1}<em> </em>(13)<em>  with 5 to go from </em>f^{-1} (f^{-1} (13))<em> to </em>f^{-1} (5)<em> </em>

<em>Then we repeat the process of using the table. Locate 5 in the f(x) row. This is in the last column. The value above that is x = -9.</em>

<em>So f(-9) = 5 and </em>f^{-1} (5)=-9

<em>Overall, </em>f^{-1} (f^{-1} (13))=-9

===============================================

Part 2

Answer:  -13

---------------------------

Explanation:

Same idea as before. Locate 8 in the f(x) row. The value above this is x = -13

<em>This means f(-13) = 8 and </em>f^{-1}(8) =-13

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