Question

http://screencast.com/t/rq9VS8fO

I don't know where to begin for B.

Answer 1

Raphael: Hello! Have you worked with inverse functions before?

Answer 2

Yes, I have! I'm just not sure how to read this question, nor write it.

Answer 3

If it's any comfort, I've found the question to be strangely worded also.
Suppose I gave you the simple function f(x)=x^3. Would you be able to find the inverse of this function? If so, please do it.

Answer 4

Cool. You know your stuff.
Now let's go back to the original function: y=x^3. Let x=2. Find y. Write the resulting point in the format (x,y).

Answer 5

(2, 8)

Answer 6

Perfect. Note the order of this ordered pair: (2,8).
Now please go back to the inverse function you found. let the independent variable = 8. what's the resulting y?

Answer 7

2

Answer 8

Yes. Now please write your new point in the same form as before: (x, y), as pertains to the inverse function you've found.

Answer 9

(8, 2)

Answer 10

Right. Now look: If you go back to the original example I gave you, y=x^3, and let x=2, you get the point (2,8).
If you yourself find the inverse function of my function, and you substitute 8, you get 2, or the point (8,2). With me so far?

Answer 11

Yeah

Answer 12

Cool. So, let's now summarize. Supposing that someone knocks on the door and gives you a function f(x), and I ask you to evaluate f(a). You end up with a point that looks like (a, f(a)). Agreed?

Answer 13

Yeah

Answer 14

Now suppose you get the point (c,d) from doing that.
Now your cousin comes knocking on the door and offers to find the inverse of my functin f(x). You take that y-coordinate d and use it as the input to the inverse function. The inverse function will take on what value?

Answer 15

Raphael: Still there?