Thursday, July 26, 2012

Single Variable Calculus, Chapter 7, 7.1, Section 7.1, Problem 2

a.) How is the inverse function f1 defined if f is a one-to-one function with domain A and range B? What is the domain of f1? What is the range of f1?
b.) If you are given a formula for f, how do you find a formula for f1?
c.) If you are given the graph of f, how do you find the graph of f1?

a.) If f is a function with domain A and range B, then f1 has domain B and range A. Thus, f1 is defined as f1(y)=x or f(x)=y
b.) If we have an equation y=f(x), we solve the equation for x in terms of y first, then replace x and y. Thus we get the inverse function f1(x).
c.) Suppose that the graph of f is given, the graph of f1 can be obtained by reflecting the graph of f about the line y=x

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