Transposing Math Functions

Introduction to transposing math functions:

            Transposing math functions involves the process of interchanging or converting one form of the given function into another form. For example the non linear function is transposed into linear form and the polynomial function is converted into normal function form. The math functions mainly deals with linear and non linear functions. Transposing of linear and nonlinear functions is carried out below with the help of certain operations. The following are the example problems for transposing math functions.

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Transposing math functions example problems:

Example 1:

Transpose the given math functions and find the coefficient value.

Sqrt (3 u + 1) = u - 3

 

Solution:

Given equation is
sqrt (3 u + 1) = u - 3

Let us squaring on both sides, then the above equation becomes 
[sqrt (3 u + 1) ] ² = (u - 3) ²

Solve the above equation 
3 u + 1 = u ² - 6 u + 9

Write the above equation in factor form. 
u ² - 9 u + 8 = 0

The above form is a quadratic equation with 2 solutions 
u = 8 and u = 1

Example 2:

Transpose the given math functions and find the coefficient value.

                    f(u) = u ³ – 48u + 5

Solution:

Given function is

f(u) = u ³ – 48u + 5

The math function of f is the set of all real numbers. The derivative f ' is given as

f '(u) = 3 u ² - 48

f '(u) is defined for all real numbers. Let us now solve f '(u) = 0 

3 u ² - 48 = 0

Add 48 on both sides,

 3 u ² – 48 + 48 = 48

    3 u ² = 48

       u ² = 16
u = 4 or u = -4

Since u = 4 and u = -4 are the coefficient value.

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Transposing math functions practice problems:

1) Transpose the given math functions and finds the coefficient value.

                      u ² – 4u + 13 =  0

Answer: u = 2 + 3i or u = 2- 3i.

2)  Transpose the given math functions and finds the coefficient value.

               2 u ² + u - 6 = 0

Answer: u = -2 or u = 3/2