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Additional Mathematics
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Additional Mathematics
Inverse Functions
Additional Mathematics
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Inverse Functions
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Inverse function
The reversal of a function such that every element in the codomain is mapped to only one element in the domain
If two functions f and g are inverse functions of each other
then, the domain of f=range of g and domain of g=range of f
If two functions f and g are inverse functions of each other
then the graph of g is the reflection of the graph of f at the line y=x
Properties of inverse function (1)
Only restricted to one-to-one function which has inverse function
Properties of inverse function (2)
fg(x)=gf(x)=x, where g(x) is the inverse function of f(x)
Properties of inverse function (3)
Graph of f inverse is the reflection graph of f in the line y=x and vice versa
Properties of inverse function (4)
If the point (a,b) lies on the graph of f then the point (b,a) lies on the graph of f inverse
Step 1 of determining the inverse function
Change function y=f(x) to the form x=f(y)
Step 2 of determining the inverse function
Write as
Step 3 of determining the inverse function
Replace variable y with variable x
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Inverse Functions
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