%5E1%2F2.jpeg "(x-2)^1/2")
Understanding the Expression (x - 2)^(1/2)
The expression (x - 2)^(1/2) represents the square root of (x - 2). Let's break down the components and explore its significance:
Understanding Exponents
- Exponent: The superscript number, in this case, (1/2), indicates the power to which the base is raised.
- Base: The base of the expression is (x - 2), representing a variable or a value.
Fractional Exponents: When the exponent is a fraction, it signifies a root. The denominator of the fraction indicates the type of root. In this case, the denominator is 2, indicating a square root.
Interpreting the Expression
Therefore, the expression (x - 2)^(1/2) is equivalent to:
- √(x - 2) which means the square root of the quantity (x - 2).
Domain and Range
Domain: The domain refers to the possible input values (x-values) for which the expression is defined. Since we cannot take the square root of a negative number, the expression is only defined for x ≥ 2.
Range: The range represents the possible output values (y-values). The square root function always outputs non-negative values, meaning the range of the expression is y ≥ 0.
Applications
The expression (x - 2)^(1/2) finds applications in various mathematical concepts and real-world scenarios, including:
- Solving equations: It may appear in equations that involve square roots.
- Graphing functions: The expression defines a function whose graph is a curve starting at the point (2, 0) and extending upwards to the right.
- Geometry: It can be used to calculate the length of a diagonal in a rectangle or the distance between two points in a coordinate plane.
Key Points to Remember:
- The expression (x - 2)^(1/2) represents the square root of (x - 2).
- The expression is only defined for x ≥ 2.
- The range of the expression is y ≥ 0.
- It has applications in various mathematical concepts and real-world scenarios.
By understanding the components and significance of this expression, you gain a deeper appreciation for its role in various mathematical contexts.