Transcript
Inverse Function
Today’s Outline
o Inverse function
o History behind function
o Finding Inverse of a function
o Application
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What is Function ?
A function is a mathematical process that uniquely relates the value of one variable to the value of one or more other variables.
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FunctionY=f(x)
Input variables
XOutput variable
Y
Example
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Historical Background
Galileo gave the statements of dependency of one on another.
In 1673 Leibnitz used the word ‘function’.
In 1734 the notation f(x) was introduced by Euler.
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What is Inverse Function ?
Let f be a function with domain D and range E. The inverse of f is the function f-1 defined by:
f-1 (b) = a where a is chosen so that f(a)=b
So, f-1 (f(x)) = xf(f-1 (x)) = x
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What functions are Invertible ?
In order for f-1 to be a function there must be only one a in D corresponding to each b in E.
Such functions are called one to one. The graph of such functions passes horizontal line test. If f is continuous, then f-1 is continuous too.
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One to one Functions
Every element of the
range corresponds to
exactly one element
of the domain.
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Why all functions don’t have Inverse ?
All functions are not one to one functions.
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Why all functions don’t have Inverse ?
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A
B
C
D
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3
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Why all functions don’t have Inverse ?
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1
2
3
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A
B
C
D
No longer a function
Steps for Finding Inverse
Stick y for f(x)
Switch x and y
Solve for y
Replace y with f-
1
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Problem13
Solution
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Solution
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Application
Let f be the function that converts a temperature in degrees Celsius to a temperature in degrees Fahrenheit.
F = f(c) = 9/5 * C + 32
C = f-1 (F) = 5/9 * (F-32)
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Any Query ?
Thank you
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