Question

How do you find the domain of validity?

Answer 1

Finding the domain of validity
Finding the domain of validity

Tips of finding the domain of validity

A function f : A ----> B is called a real valued function, If B is a subset of R ( set of all real numbers ).

If A and B both are subsets of R, then f is called a real function.

In other words, A function whose range is in the real numbers is said to be a real function, also called a real-valued function.

Steps for finding the domain and range of a function:Step 1 : Put y = f(x) .Step 2 : Solve the equation y = f(x) for x in terms of y. Let x = p(y) .Step 3 : Find the values of y for which the values of x , obtained from x = p (y) are real and in the domain of f.Step 4 : The set of values of y obtained in above step is the range of f.

Find the domain of real valued functions : f(x) = 1x−21x−2

Solution : Here x can take any real number except 2. Since at x = 2 the denominator would become zero and divisible by zero is not defined . 

Hence domain in interval notation is given by :

Domain: (-∞∞, 2) ∪∪ ( 2, +∞∞ ) OR Domain: R - { 2 }.

Use the below widget to find the domain and range of a function.