Question

What is $f\left( 3 \right)$ if $f\left( x \right)=2x+4$ ?

Answer 1

Hint: We can find the output of only that input of a function if the input is a part of the domain of that function. So, first we will find the domain of the given function. Then we will satisfy $3$ in place of $x$ in the function by replacing $x$ by $3$.

Complete step by step solution:
A function is a relation between the input and output where every input has a unique output. The input is termed as the domain and the output is termed as the range of the function. Every element that lies in the domain of the function always satisfies the function.
Here, the function is defined as
$f\left( x \right)=2x+4$
Since, it is a polynomial function, it exists for all real values of $x$ . Thus,
Domain of $f\left( x \right):\text{ }x\in R$
We need to find the value of the function at $x=3$ , which exists because $3$ is a real number. So, we will replace $x$ by 3 in the given function $f\left( x \right)$ ,
$\begin{align}
  & f\left( 3 \right)=2\left( 3 \right)+4 \\
 & \Rightarrow f\left( 3 \right)=6+4 \\
 & \Rightarrow f\left( 3 \right)=10 \\
\end{align}$
So, the value of $f\left( x \right)$ corresponding to $x=3$ is $10$ .

Hence, for $f\left( x \right)=2x+4$, $f\left( 3 \right)$ is equal to 10.

Note: We can find the value of a function only when the input lies in the domain of that function. Otherwise, we will obtain an indeterminate form and cannot obtain the output.
For example,
$f\left( x \right)=\dfrac{1}{x-1}$
Here, the domain of $f\left( x \right):\text{ }x\in R-\left\{ 1 \right\}$
Here, $x=1$ does not lie in the domain of $f\left( x \right)$ . Hence, we cannot find $f\left( 1 \right)$ as the function’s value at $x=1$ will tend to infinity, which is an indeterminate value.