Question

How do you find the domain of the function$f\left( x \right) = \dfrac{3}{{x + 2}}$?

Answer 1

Hint: This question deals with the concept of domain and range. Before solving the question, we should know what is domain and range. The domain refers to the set of possible values of x for which the function will be defined and the range refers to the possible range of values that the function can attain for those values of x which are in the domain of the function. Here in this question, we need to find the domain of the given function.

Complete step by step solution:
Given function is$f\left( x \right) = \dfrac{3}{{x + 2}}$
We have to find the domain of a given function.
Let us try to solve the given question, first we put the denominator of the given function equal to zero.
$
   \Rightarrow x + 2 = 0 \\
   \Rightarrow x = 0 - 2 \\
   \Rightarrow x = - 2 \\
 $
So, domain: $x \ne - 2$
Therefore, the domain of $f\left( x \right) = \dfrac{3}{{x + 2}}$in
Interval Notation: $\left( { - \infty , - 2} \right) \cup \left( { - 2,\infty } \right)$
Set-Builder Notation: $x < - 2$or$x > 2$

Note: The given question is an easy one. Students should solve such types of questions very carefully. An independent set of those values for a given function which on substitution always gives real value of result but set of value of range is depending upon the value of the set of domains as it is necessary that all ranges must have domain is known as domain. When a function is defined, its domain and co-domain are also mentioned. The domain and co-domain need not be different. They may be the same as well. Students can find similar types of questions in their NCERT textbooks and practise them for more clarity.