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1.4 Inverses of Functions.notebook
1
September 19, 2016
The function is onetoone, because no output is ever used more than once in the
function's pairings.
yes, each input has exactly one output
The function is manytoone because inputs 1 and 4 have the same output 2
The inverse relation is not a function because the input 2 has two outputs, 1 and 4
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The graphs reflect across the line y=x, which makes sense because the ordered pairs
in a function and its inverse have their x and y coordinates reversed
The outputs of f1(f(x)) exactly match the inputs of f1(f(x)). This means f1(f(x))= X. The
original function takes an input and assigns an output. The inverse picks up that output and
uses it as an input. The inverse turns around and has an output equal to the original input.
The range of the original is the domain of the inverse, and the range of the inverse is the
domain of the original.
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The lines intersect along y=x. This means the original and inverse are the same at this point
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It must be onetoone
An inverse undoes these operations. Therefore it performs the inverse operation in
reverse order
If f(g(x))= x and g(f(x))=x then f(x) and g(x) are inverse functions
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