Function Questions

Question

If the domain of a function f(x) is the set {10, 20, 30}. What does the information tell you about f^-1(x)?

If the graph of a function f(x) includes the point (3, 0), what point must the graph of f^-1(x) include? Explain.

Answer 1

f^-1 means 1 over; so you have1/10, 1/20, 1/30.

The graph of 1/x includes (3, .38).

Answer 2

A function is defined as a set of ordered pairs. The domain of a function is the set of first elements of the ordered pairs. Our function has a domain of {10, 20, 30}, which means that the function is defined by the ordered pairs (10,a), (20,b), and (30,c), where a, b, and c have some unknown values.

The f^-1(x) notation usually indicates that we are talking about an inverse function. The inverse function is defined by the same ordered pairs, with the first and second elements reversed. That is, the inverse function is defined by the ordered pairs (a,10), (b,20), and (c,30), in this exercise.

(Actually, the "inverse function" may not be a function at all, but let's talk about that another time.)

To answer the 2nd part of the question, it should now be clear that if some other function g includes the point (3,0), then g^-1 must include the point (0,3).