Question

How do you find the domain of $h(x) = \dfrac{1}{{x + 1}}$

Answer 1

Hint:In this question, we are given a function and we have to find its domain. A function is defined as an algebraic expression that contains two unknown variables and one of the variables is expressed in terms of the other variable. The domain of the function is defined as all the possible values that x actually takes, that is, the values of the x for which a function is defined is called the domain of the function. Using the above-mentioned definition of domain and the knowledge of fractions, we can find out the domain of the given function.

Complete step by step answer:
We are given that $h(x) = \dfrac{1}{{x + 1}}$
We know that for a fraction to exist, its denominator can take any value except zero, so –
$
x + 1 \ne 0 \\
\Rightarrow x \ne - 1 \\
$
So, the domain of $h(x)$ is all real numbers except -1.

Note: The set of all the values from which we can choose the value of x is known as the codomain of the function and we obtain different values of the function by putting different values from the domain, thus the range is defined as the set of all the possible values that a function can attain. So we should not get confused between the definition of codomain, domain and range of a function. Thus we must know the concept of the domain and range of function clearly for solving this kind of question.
In this question, we knew that the denominator cannot be zero that’s why we could get the correct answer easily.