Suppose f(x)= 3x-5.

Question

What are the domain and range of f?
Find f-1(x).
What are the domain and range of f-1(x)? Be careful!
Find (ff-1)(x) and (f-1f)(x). What do you notice?
Graph the functions f and f-1. Is there a solution to f= f-1?

Answer 1

Domain of f: All real numbers
Range of f: All real numbers

f-1(x) = (x+5)/3

Domain of f-1: All real numbers
Range of f-1: All real numbers greater than or equal to -5/3

(ff-1)(x) = x
(f-1f)(x) = x

The graphs of f and f-1 intersect at the point (0,0). This is the only solution to f=f-1.

Answer 2

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