Section 1.5 Inverse Functions

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Presentation transcript:

Section 1.5 Inverse Functions domain of f(x) = range of f-1(x) range of f(x) = domain of f-1(x) when you compose f(x) and f-1(x) you will get the identity function f(f-1(x))= f-1(f(x))=x ex. f(x)=4x, f-1(x) = x/4

Steps to find the inverse of a function (rule #13) 1. replace f(x) with y 2. switch x and y 3. solve for y 4. replace y with f-1(x) ex. f(x) = x+4

Verifying Inverse Functions Which of the functions is the inverse of f(x)= 5/(x-2) ? g(x) = (x-2)/5 h(x) = (5/x) + 2

Graphing Inverse Functions The inverse is a reflection across the y = x line If (a,b) lies on the graph of the function, then (b,a) lies on the graph of the inverse. Sketch the graph and its inverse f(x) = 2x-3 A function f has an inverse iff no horizontal line intersects the graph of f at more than one point. This is the horizontal line test.