Inverse Function Worksheet
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Inverse Function Worksheet
Inverse function are define as the functions that undoes the another functions. In
mathematics these functions are defined for eliminating the working of other functions
on which these inverse functions are defined .
We can understand it by a simple example is that if we take a variable p into a
function f and it gives the output q and according to the inverse function if there is an
another function s that gives the output p when entering the input q are known as the
inverse functions to each other.
If a function that has inverse is also known as invertible function. If there is function f
then its inverse function is define as the 1 / f that is also written as f 1.
According to the definition of the inverse function if there is a function that has the
input and produces the output and another function that takes the output of first
function as input and produces output equals to the input of the first function known
as inverse of the functions. It is represented in the form as f (a) = b then
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g (b) = a is the inverse function of f (a).
We can take an example of defining the process of inverse function as if there is a
function
p (a) = 2 a + 3 then inverse of the function is as in the first function p (a) there is
variable a is multiplied with 2 and also constant value 3 is added to 2 a that is given
the expression 2 a + 3 and for making the inverse of the given function first we have
to subtract the 3 and then divide the term by 2 as
q (b) = b  3 / 2 that is the inverse of the function p (a) = 2 a + 3. So we can written
the function as
p (a) = 1 / q (b) and inverse function of the p (a) = 2 a + 3 is describe as p 1 (b) = (b 
3) / 2 .We are using the term b in place for showing that we use the different values.
If we take some values in the above define functions as p (a) = 2 * a + 3 ,
If a = 4 then p (4) = 2 * 4 + 3
p (4) = 8 + 3 = 11.
Then according to the inverse function depiction if we take the input for the function q
(b) = (b  3) / 2 is 11 as q (11) = (11  3) / 2
q (11) = (8) / 2
q (11) = 4.
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So we can see that for inputting the answer of first function we can get the output
equals to the input of first function as describe in the definition of the inverse function.
We can use the inverse function in solving the algebra problems as if there is a
function f (a) = 2 a + 3 and if we put the variable b in place of f (a) that is depicted as
b = 2 a + 3 and then subtracted 3 from both side of equation as
b  3 = 2 a + 3  3
b  3 = 2 a
and then divide both side of equation by 2 as b  3 / 2 = 2 a / 2
b  3 / 2 = a
It is also written as a = (b  3) / 2
So it is shows as in form of inverse function f 1 (b) = (b  3) / 2 .
inverse function worksheet has several examples for defining the inverse functions.
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