Question

How do you calculate $f\left( x \right)$ for the given domain values$f\left( x \right)=4x+8$ ; $x=1,11,21,31,101$ ?

Answer 1

We have to calculate the function values of a given function for certain domain values. We solve the given question by simply substituting the domain values in the given function and then evaluate the expression to find the final answer.

Complete step by step answer:
We are given a function and need to calculate the value of the function for different domain values. We will be solving the given question by simply substituting the value of domain in the given function.
The function is $f\left( x \right)=4x+8$
According to the question,
The function has to be calculated for the following domain values,
$x=1,11,21,31,101$
The domain of a given function or any function, in general, in general can be defined as the set of those values for which the function is defined and has some real values.
Now, we need to substitute the given domain values one by one and simplify to get the answer.
For the value of $x=1$ ,
$f\left( x \right)=4x+8$
Substituting the value $x=1$ in the function and simplifying the expression, we get,
$\Rightarrow f\left( 1 \right)=4\times 1+8=12$
For the value of $x=11$ ,
$f\left( x \right)=4x+8$
Substituting the value $x=11$ in the function and simplifying the expression, we get,
$\Rightarrow f\left( 11 \right)=4\times 11+8=52$
For the value of $x=21$ ,
$f\left( x \right)=4x+8$
Substituting the value $x=21$ in the function and simplifying the expression, we get,
$\Rightarrow f\left( 21 \right)=4\times 21+8=92$
For the value of $x=31$ ,
$f\left( x \right)=4x+8$
Substituting the value $x=31$ in the function and simplifying the expression, we get,
$\Rightarrow f\left( 31 \right)=4\times 31+8=132$
For the value of $x=101$ ,
$f\left( x \right)=4x+8$
Substituting the value of $x=101$ in the function and simplifying the expression, we get,
$\Rightarrow f\left( 101 \right)=4\times 101+8=412$
Therefore, $f\left( x \right)$ for the given domain values $x=1,11,21,31,101$ is:
For$x=1$ $\Rightarrow f\left( 1 \right)=12$
For $x=11\Rightarrow f\left( 11 \right)=52$
For $x=21\Rightarrow f\left( 21 \right)=92$
For $x=31\Rightarrow f\left( 31 \right)=132$
For $x=101\Rightarrow f\left( 101 \right)=412$

Note: We must remember the following points while finding the domain of any function,
1. The denominator of a fraction cannot be zero.
2. The expression under a root sign should be positive.
The range of a function can be defined as the set of all the possible outcomes of the functions for its domain. We can calculate the values of the range by substituting the values of the domain in the given function.