How To Find Domain Of Square Root

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 bug 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 divers past an expression with variable x, the implied domain of f is the set of all real numbers variable x tin can accept such that the expression defining the role is real. The domain can likewise be given explicitly.
For a square root role given by f(x) = √ten to take real values, the radicand x must be positive or equal to cipher.
besides Step by Step Calculator to Discover 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 - i)

Solution to Example one

• For f(x) to accept real values, the radicand (expression under the radical) of the square root function must be positive or equal to 0. Hence
  x - 1 ≥ 0
  
• The solution ready to the higher up inequality is the domain of f(x) and is given by: x ≥ 1
  or in interval grade [ane , +∞)
  

Matched Problem 1:

Find the domain of role f defined past

f(10) = √(x + 5)

Instance 2

Find the domain of office f defined by

f(x) = √ [ (x - 2)(10 + 3) ]

Solution to Example two

• For f(10) to have real values, the radicand (x - 2)(10 + iii) must be positive. Hence
  (x - two)(x + three) ≥ 0
• Solve the above inequality to obtain the solution set, which is also the domain, in interval form as follows:
  (-∞ , -3] ∪ [2 , + ∞)

Matched Problem 2:

Notice the domain of part f defined past:

f(ten) = √ [ - x (x + 1) ]

Example three

Detect the domain of function f divers by:

f(x) = √ [ x² + 2 x - 1 ]

Solution to Example 3

• For √ [ 10² + 2 x - i ] to be existent, the radicand must be positive or equal to 0. Hence the inequality
  10 ^two + 2x - 1 ≥ 0
  
• The solution gear up of the higher up inequality, which is too the domain, is given in interval class equally follows:
  (-∞ , -one-√2] ∪ [-i+ √2 , + ∞)
  
• The domain of the given role is given past the interval (-∞ , -ane-√ii] ∪ [-1+ √2 , + ∞).
  

Matched Problem iii:

Detect the domain of part f divers past:

f(x) = √[ - 3 x ² - x + 4 ]

Example four

Find the domain of function f defined by:

f(ten) = √[ (2x - ane)/(x + iii) ]

Solution to Instance 4

• The domain of this function is the ready of all values of 10 such that (2x - ane)/(10 + 3) ≥ 0 which is an inequality to solve. The solution set of the above inequality which is also the domain is given past
  (-∞ , -3) U [ 1 / 2 , +∞)

Matched Problem 4:

Find the domain of function f defined by:

f(x) = √[ (- x + 1)/(3x - 2) ]

Example v

Find the domain of function f defined by:

f(ten) = √[ |-2 x - 6| ]

Solution to Case 5

• The domain of this function is the set of all values of x such that |-two 10 - vi| ≥ 0. Nosotros demand to solve the inequality
  |-two x - 6| ≥ 0
  
• Because of the accented value, the expression |-two ten - 6| is greater than or equal to 0 for all existent numbers. Hence the domain of the to a higher place function is given by:

  (-∞ , +∞)

Matched Problem 5:

Find the domain of office f defined by:

f(x) = √[ | - ten + 8| ]

Answers to the Matched Problems Above

1. [-5 , +∞)
2. [-ane , 0]
3. [-4/3 , 1]
4. (ii/3 , 1]
5. (-∞ , ∞)

More than References and Links

Pace by Footstep Solver to Find the Domain of the Foursquare 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 .

Source: https://www.analyzemath.com/DomainRange/find_domain_squareroot.html

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