Question

Find the function values $f\left( 0 \right)$given$f\left( x \right) = - 4x$.

Answer 1

Hint: A Function can be described as a set of inputs with a single output in every case. Every function has a domain and range. The domain is the set of all possible values of\[x\]which will satisfy the function and the range of a function is the complete set of all possible resulting values of the output variable $y$ which is obtained after substituting the domain. So here with the help of basic definition and properties of a function we can solve the given question.

Complete step-by-step solution:
Given
$f\left( x \right) = - 4x................................\left( i \right)$
So here we have been given $f\left( x \right) = - 4x$ such that we have to find the function value $f\left( 0 \right)$. Now in simple terms it can be said that it simply means we have to find the value of $f\left( x \right) = - 4x$ at $x = 0$.
So in order to find the function value $f\left( 0 \right)$ we just have to substitute $x = 0$ in the given function which is in equation (i):
So on substituting $x = 0$in (i) we can write:
$
   \Rightarrow f\left( x \right) = - 4x \\
   \Rightarrow f\left( 0 \right) = - 4 \times 0 \\
   \Rightarrow f\left( 0 \right) = 0....................................\left( {ii} \right) \\
 $

Therefore the function values$f\left( 0 \right)$for$f\left( x \right) = - 4x$ would be $0$.

Additional information:
Function notation is a way in which a function can be represented using symbols and signs. Function notation is used for simple representation of a function instead of lengthy written explanation.

Note: Now similar questions involving value of functions are to be solved as above. In order to identify an element of a function to be examined function notations are of great use. Also one should be careful while substituting values in a given equation for finding the value at a given point.