6.2 InverseFunctions

# 6.2 InverseFunctions - MAC1140, MAC1147 6.2: One-to-One...

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MAC1140, MAC1147 6.2: One-to-One Functions; Inverse Functions If f( x ) = y is a function, its inverse f –1 ( x ) is f( y ) = x , where y becomes the domain and x becomes the range. If for each y in the domain of the inverse function there is a unique x in the range, it is a one-to-one function . If a horizontal line intersects the graph of a function f no more than once, then f is one-to-one. Only one-to-one functions have inverses. We can verify that f and f –1 are inverses showing that f ( f –1 (x)) = f -1 ( f (x)) = x . The graph of a function f and its inverse f –1 are symmetric with respect to the line y = x . To find the inverse of a function y = f(x), interchange x and y to obtain x = f(y) and solve for y in terms of x . Is the following a one-to-one function? If so, find the inverse and state its domain and range. Gallons Cost 5 \$12.50 10 \$25 15 \$37.50 20 \$50 2. y = x 2 (1, 1) (-1, 1) Use the horizontal line test to see whether f is one-to-one; if yes, graph its inverse:

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## This note was uploaded on 01/04/2012 for the course MAC 1147 taught by Professor Staff during the Fall '08 term at Miami Dade College, Miami.

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6.2 InverseFunctions - MAC1140, MAC1147 6.2: One-to-One...

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