Definition Non Linear

In math, a nonlinear system is one of the system which is not linear, that is, a system which does not assure the superposition principle, or whose result is not directly proportional to its input. The equation used to solve the non linear problem is f(x)=C. This function is called as linear if f(x) is a non linear. This article gives some of the examples about the non linear by using this definition.


Examples of Definition Non Linear:

By using the definition of non linear solve the following examples.

Example problem1:

Use the following function rule to find f(7).

`f(x)=2x^2`

Solution:

Given `f(x)=2x^2` ; Find f(7).

Plug x = 7 into the function and simplify.

`f(x) = 2x^2`

`f(7) = 2(7)^2`            Plug in x = 7

f(7) = 2(49)                  Square

f(7) = 98                       Multiply

Which is the required solution.

Example problem2:

Use the following function rule to find f(8).

`f(x) = (x - 4)^2`

Solution:

Given:

`f(x) = (x - 4)^2`

Find: f(8)

Plug x = 8 into the function and simplify.

`f(x) =(x - 4)^2`

`f(8) = ( 8 - 4)^2`            Plug in x = 8

`f(8) = (4)^2`                  Subtract

f(8) = 16                          Square

Which is the required solution.

Example problem3:

Use the following function rule to find f(1).

f(x) = 5 – 4|x|

Solution:

Given: f(x) = 5 – 4|x|; Find f(1)

Plug x = 1 into the function and simplify.

f(x) = 5 –4|x|

f(1) =5 – 4|1|                  Plug in x = 1

f(1) =5 – 4(1)                 Take the absolute value

f(1) =5 – 4                       Multiply

f(1) = 1                            Subtract

Which is the required solution.

Practice Problems of Definition Non Linear:

Problem 1:

Use the following function rule to find f(7).

f(x) = -9|x| + 4

Solution:

f(7) = -59

Problem 2:

Use the following function rule to find f(-8).

`f(x) = 3x^2`

Solution:

f(-8) = 192