Introduction to determining a linear function:
Determining the linear function involves the process of finding linear function by solving the equations in non linear form. The linear function deals with basic linear equation and it satisfies all the terms and conditions of the linear algebra. Linear algebra mainly involves finding the system o equations with the known values. Linear function has the demonstration in analytical geometry and generalized in operator theory. The examples are discussed below for determining linear function whereas linear function associates with the families of vector called linear spaces. The following are the example problems to determine linear function.
Examples for Determining a Linear Function:
Example 1:
Determine the linear function from the given function.
f(a) = a 2 – 15a + 18
Solution:
The given function is
f(a) = a 2 – 15a + 18
To find the linear function, differentiate the given function.
f '(a) = 2a – 15
Conclusion: f '(a) = 2a – 15 is the determined linear function.
Example 2:
Determine the linear function from the given function.
f(x) = 5x 2 – 2x + 6
Solution:
The given function is,
f(x) = 5x 2– 2x + 6
To find the linear function, differentiate the given function.
f '(x) = 2(5x) – ( 2 )
f '(x) = 10x – 2
Conclusion: f '(x) = 10x – 2 is the determiner linear function.
Example 3:
Determine the linear function from the given function.
f(x) = 3x 3 – 5x 2 + 10x - 3x 3 + 5x 2 + 11x + x 4 – x 4 + 18 + 5
Solution:
Given expression is,
f(x) = 3x 3 – 5x 2 + 10x - 3x 3 + 5x 2 + 11x + x 4 – x 4 + 18 + 5.
Arrange the above expression in order.
f(x) = x 4 – x 4 + 3x 3 – 3x 3 - 5x 2 + 5x 2 + 11x + 10x + 18 + 5.
Cancel the common terms from the above equation.
f(x) =11x + 10x + 18 + 5.
Grouping the above terms
f(x) =21x + 23.
Conclusion: f(x) =21x + 23 is the determined linear function.
Practice Problems for Determining a Linear Function:
1) Determine the linear function from the given function.
f(y) = 8y 2– 5y + 16
Answer: f '(y) = 16y – 5.
2) Determine the linear function from the given function.
f(x) = 4x 2 – 5x 3 + 4x - 4x 2 + 5x 3 + 6x + 12 + 5
Answer: f(x) = 10x + 17
Determining the linear function involves the process of finding linear function by solving the equations in non linear form. The linear function deals with basic linear equation and it satisfies all the terms and conditions of the linear algebra. Linear algebra mainly involves finding the system o equations with the known values. Linear function has the demonstration in analytical geometry and generalized in operator theory. The examples are discussed below for determining linear function whereas linear function associates with the families of vector called linear spaces. The following are the example problems to determine linear function.
Examples for Determining a Linear Function:
Example 1:
Determine the linear function from the given function.
f(a) = a 2 – 15a + 18
Solution:
The given function is
f(a) = a 2 – 15a + 18
To find the linear function, differentiate the given function.
f '(a) = 2a – 15
Conclusion: f '(a) = 2a – 15 is the determined linear function.
Example 2:
Determine the linear function from the given function.
f(x) = 5x 2 – 2x + 6
Solution:
The given function is,
f(x) = 5x 2– 2x + 6
To find the linear function, differentiate the given function.
f '(x) = 2(5x) – ( 2 )
f '(x) = 10x – 2
Conclusion: f '(x) = 10x – 2 is the determiner linear function.
Example 3:
Determine the linear function from the given function.
f(x) = 3x 3 – 5x 2 + 10x - 3x 3 + 5x 2 + 11x + x 4 – x 4 + 18 + 5
Solution:
Given expression is,
f(x) = 3x 3 – 5x 2 + 10x - 3x 3 + 5x 2 + 11x + x 4 – x 4 + 18 + 5.
Arrange the above expression in order.
f(x) = x 4 – x 4 + 3x 3 – 3x 3 - 5x 2 + 5x 2 + 11x + 10x + 18 + 5.
Cancel the common terms from the above equation.
f(x) =11x + 10x + 18 + 5.
Grouping the above terms
f(x) =21x + 23.
Conclusion: f(x) =21x + 23 is the determined linear function.
Practice Problems for Determining a Linear Function:
1) Determine the linear function from the given function.
f(y) = 8y 2– 5y + 16
Answer: f '(y) = 16y – 5.
2) Determine the linear function from the given function.
f(x) = 4x 2 – 5x 3 + 4x - 4x 2 + 5x 3 + 6x + 12 + 5
Answer: f(x) = 10x + 17
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