Homework 11:
Due Wednesday 7/7/14
x
1
2
3
4
5
f(x)
3
-2
4
5
1
g(x)
5
2
6
4
5
1. The chart above defines two functions f and g. Which (if any) of these functions are
invertible? Why?
1
2. If f (x) = x + 4, find f −1 (x). What is f −1 (5)? What is f (f −1 (5))?
2
3. In number 2 above, f and f −1 are both lines. What is the relationship between the
slope of f and the slope of f −1 ? Do you think you could show that this relationship is
true for any line y = mx + b? If so you can try it as a bonus if you want.
4. If f (x) = 2x find f −1 (x).
1
5. If f (x) = x find f −1 (x).
8
Bonus: With numbers 4 and 5 in mind can you think of a funtion that is its own
inverse? Are there other such functions?
1