How to Find the Domain of Square Root Functions?

A step by step tutorial, with detailed solutions, on how to find the domain of square root functions is presented. Matched problems to the exercises with solutions at the bottom of the page are also presented.

Definition of the Domain of a Function

For a function f defined by an expression with variable x, the implied domain of f is the set of all real numbers variable x can take such that the expression defining the function is real. The domain can also be given explicitly.
For a square root function given by f(x) = √x to have real values, the radicand x must be positive or equal to zero.
also Step by Step Calculator to Find Domain of a Function

Examples on How to Find the Domain of Square Root Functions with Solutions

Example 1

Find the domain of function f defined by
f(x) = √(x - 1)

Solution to Example 1

Matched Problem 1:

Find the domain of function f defined by
f(x) = √(x + 5)

Example 2

Find the domain of function f defined by
f(x) = √ [ (x - 2)(x + 3) ]

Solution to Example 2

Matched Problem 2:

Find the domain of function f defined by:
f(x) = √ [ - x (x + 1) ]

Example 3

Find the domain of function f defined by:
f(x) = √ [ x2 + 2 x - 1 ]

Solution to Example 3

Matched Problem 3:

Find the domain of function f defined by:
f(x) = √[ - 3 x 2 - x + 4 ]

Example 4

Find the domain of function f defined by:
f(x) = √[ (2x - 1)/(x + 3) ]

Solution to Example 4

Matched Problem 4:

Find the domain of function f defined by:
f(x) = √[ (- x + 1)/(3x - 2) ]

Example 5

Find the domain of function f defined by:
f(x) = √[ |-2 x - 6| ]

Solution to Example 5

Matched Problem 5:

Find the domain of function f defined by:
f(x) = √[ | - x + 8| ]

Answers to the Matched Problems Above

  1. [-5 , +?)
  2. [-1 , 0]
  3. [-4/3 , 1]
  4. (2/3 , 1]
  5. (-? , ?)

More References and Links

Step by Step Solver to Find the Domain of the Square Root of a Linear Function
Find domain and range of functions,
Find the range of functions,
find the domain of a function and mathematics tutorials and problems.