Slide 6.1.pptx - Inverse Function Definition A function f...

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Inverse Function
DefinitionA function f with domain D and range R is a one-to-one function if whenever a ≠ b in D, then f(a) ≠ f(b) in R.If f(x) is a one-to-one function with domain D and range R, then a function g with domain R and range D is its inverse function with the condition:xDbaf(x)f(b)Rf(a)
Horizontal Line TestIf the graph of a function y = f(x) is such that no horizontal line intersects the graph in more than one point, then it is one-to-one and has an inverse function
Definitionf(x) and g(x) are inverse functions if:1.g(f(x)) = x for all x in the domain of f.2.f(g(x)) = x for all x in the domain of g.Example 1If f(x) = (x-1)/2 and g(x) = 2x+1, show that f and g are inverses of each other. Graph f and g.g(f(x)) = f(g(x)) =

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