A Comprehensive Guide to the Square Root Function and its Properties

f(x)=sqrt(x)

The function f(x) = sqrt(x) represents the square root function

The function f(x) = sqrt(x) represents the square root function. Let’s break down the important components and properties of this function.

Definition:
The square root of a non-negative number x is a value that, when multiplied by itself, yields x. Symbolically, the square root of x is denoted as √x.

Function Notation:
In the given function f(x) = sqrt(x), f(x) represents the output or result of the function when applied to the input value x.

Domain:
The domain of the square root function f(x) = sqrt(x) consists of all non-negative real numbers (x ≥ 0). The function is defined only for non-negative values of x, as the square root of a negative number is not a real number.

Range:
The range of the function f(x) = sqrt(x) consists of all non-negative real numbers (f(x) ≥ 0). The output or result of the square root function is always non-negative.

Graph:
The graph of the square root function, f(x) = sqrt(x), is a curve that starts from the origin (0, 0) and continues to increase as x increases. The graph is in the shape of a half-parabola opening towards the right.

Properties:
1. Square Root of Zero: The square root of zero (√0) is zero itself.
– sqrt(0) = 0

2. Square Root of One: The square root of one (√1) is one itself.
– sqrt(1) = 1

3. Square Root of Positive Numbers: The square root of a positive number is positive.
– If x > 0, then sqrt(x) > 0

4. Square Root of a Product: The square root of a product is equal to the product of the square roots of the factors.
– sqrt(a * b) = sqrt(a) * sqrt(b)

5. Square Root of a Fraction: The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator.
– sqrt(a/b) = (sqrt(a))/(sqrt(b))

Using the properties and understanding of the square root function, you can evaluate specific values or solve equations involving the function.

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