## About "Domain of a square root function"

Domain of a square root function :

Here we are going to see how to find domain of a square root function .

What is domain ?

The domain of a function is the complete set of possible values of the independent variable.

In other words, the domain of f(x) is the set of all those real numbers for which f(x) is meaningful.

To find the domain of a square root function, we need to follow the steps given below.

Step 1 :

If the square root is in numerator, we need to equate the expression inside the radical sign to ≥ 0.

If the square root is in denominator, we need to equate the expression inside the radical sign to > 0.

Step 2 :

We need to find the values of x which satisfies the above condition.

Step 3 :

Represent the solution using intervals.

Step 4 :

Write the domain using step 3.

Let us look into some example problems to understand the above concept.

Example 1 :

Find the domain of the following function

f(x)  =  √(x - 2)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to ≥ 0

x - 2 ≥ 0

Step 2 :

x - 2 + 2 ≥ 0 + 2

x  ≥ 2

Step 3 :

Possible values of x are between [2, ∞)

Step 4 :

Hence the domain of the given function is x ∈ [2, ∞)

Example 2 :

Find the domain of the following function

f(x)  = 1/ √(1 - x)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to > 0

1 - x ≥ 0

Step 2 :

Subtract 1 on both sides

1 - x - 1  > 0 - 1

-x  > -1

Divide by -1 on both sides

-x/(-1)  >  -1/(-1)

x  <  1

Step 3 :

Possible values of x are between (∞, 1)

Step 4 :

Hence the domain of the given function is x ∈ (∞, 1)

Example 3 :

Find the domain of the following function

f(x)  √(4 - x2)

Solution :

Step 1 :

Since the square root sign is in numerator, we need to equate the expression inside the radical sign to ≥ 0

4 - x2 ≥ 0

Step 2 :

4 - x2 ≥ 0

Subtract 4 on both sides

4 - x2 - 4 ≥ 0 - 4

- x≥ -4

x≤ 4 ==> x = ± 2

Step 3 :

Possible values of x are between [-2, 2]

Step 4 :

Hence the domain of the given function is x ∈ [-2, 2]

Example 4 :

Find the domain of the following function

f(x)  √(4 - x) + 1/√(x2 - 1)

Solution :

Step 1 :

The given function has two parts.

Part 1 is √(4 - x)

Part 2 is 1/√(x2 - 1)

Since part 1 is having square root sign in the numerator,  we need to equate the expression inside the radical sign to ≥  0.

4 - x  0

Since part 2 is having square root sign in the denominator ,  we need to equate the expression inside the radical sign to > 0

x2 - 1 > 0

Step 2 :

 4 - x ≥ 0Subtract 4 on both sides4 - x - 4 ≥ 0 - 4-x ≥ -4x ≤ 4 x2 - 1 > 0Add 1 on both sidesx2 - 1 + 1 > 0 + 1x2 >  1x >  ±1

Step 3 :

Possible values of x are between (-∞, -1) U (1, 4]

Step 4 :

Hence the domain of the given function is x ∈ (-∞, -1) U (1, 4]

After having gone through the stuff given above, we hope that the students would have understood "Domain of a square root function".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6