Question

How do you evaluate function notation?

Answer 1

Hint: We first define the use and the definition of function. We take an arbitrary function to explain the domain and range of the function. Then we put an arbitrary value for the function to find the functional value.

Complete step-by-step answer:
The basic requirement for a function to have input and evaluate its output. The input is called the domain of the function and the outcome is called the range.
We generally define a function as $ f\left( x \right) $ . We can also express it as
 $ f:x\to f\left( x \right) $ .
If we want to evaluate a function, we need to substitute the input (the given number or expression) for the function's variable (placeholder, x). Replace the x with the number or expression.
The example of a function is $ f\left( x \right)=a{{x}^{2}}+\log x-3 $ .
There are many types of functions like linear, quadratic, mixed function.
Let us take the function $ f\left( x \right)=a{{x}^{2}}+\log x-3 $ . We want to evaluate the functional value for $ x=1 $ . We put the value in the function
 $ f\left( x \right)=a{{x}^{2}}+\log x-3 $ and get
 $ f\left( 1 \right)=a\times {{1}^{2}}+\log 1-3=a-3 $ .
Therefore, the value 1 is the input from the domain and the value of $ a-3 $ is the output from the set of range.

Note: We have to remember the condition that the 1 input can not have more than one output as in that case it will not be defined as the function. The function can have more than 1 input and 1 single output for all of them.