Question

What is a domain restriction? And how do you find domain restrictions?

Answer 1

Hint: In the above question you were asked about what is domain restriction. A domain and range may be restricted because of several reasons. Also, the restrictions are partly dependent on the type of function. So let us see how we can solve this problem.

Complete step by step solution:
For a function f(x), we consider the real values of x for the domain. But not all the real values are considered because of certain restrictions. This is known as domain restrictions.
The reasons because of which a domain is restricted are:
We cannot divide a fraction if it has zero as its denominator.
We cannot take the square root of a negative number, because it will give us an imaginary number.
Now, let us see how we can find a domain restriction.
Suppose an equation is given which is $\dfrac{{x + 2}}{{1 - x}}$ . Now if we get x as 1 then the denominator part will become zero. Hence we cannot conclude the above equation with x as 1.
Also, if we have to find the value of $\sqrt {2 - x}$ and the value of x is greater than 2, then we will get an imaginary number.

Note:
In the above solution we get to know about domain restriction. We also see how we can find these restrictions. The domain and range are a real number but not all the real numbers can be considered within the range and domain.