Question

What is the domain and range of $ F(x) = {x^2} - 3 $ ?

Answer 1

Hint: The domain and range of the function is the defining factors of a function apart from its definition, The domain of the function is the values of the given variable which the function can take and not become undefined at those points , The range of a function is the solution set of the function in which the given function gives its output. Thus the input values that are admissible for a function can be called as the domain of that function and the output values of the function are called as the range.

Complete step by step solution:
We have to find the domain and range of the above function. Since we know polynomials can take any values in the real spectrum the domain of the function will be all real numbers for finding range we will see if the perfect square will give what negative values and what will happen to the output of the function when it does so
The domain of the given function is all real numbers since the polynomials can take all the values in the real set
We will now find the range of the function,
The square in the function
 $ F(x) = {x^2} - 3 $
Can give minimum value $ 0 $ and max value $ \infty $ but since $ - 3 $ is present
The minimum values would be $ - 3 $ and max value $ \infty $ .
Hence the range is $ [ - 3,\infty ) $

Note: The easy way to remember what domain and range Is to remember domain as the input values and the range as the output values. Thus the input values that are admissible for a function can be called as the domain of that function and the output values of the function are called as the range.