Question

Find the domain of the function. $F(p)=\sqrt{2-\sqrt{p}}$

   Find the domain of the function.
$F(p)=\sqrt{2-\sqrt{p}}$

Calculus

James Stewart 7th Edition

Chapter 1, Problem 37

Instant Answer

Solved by Expert Rajesh Routray

03/19/2020

Step 1

Step 1: To find the domain of the function $F(p)=\sqrt{2-\sqrt{p}}$, I need to identify all values of $p$ for which the function is defined. Show more…

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Find the domain of the function. $F(p)=\sqrt{2-\sqrt{p}}$

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Key Concepts

Domain of a Function

In mathematics, the domain of a function is the complete set of possible input values (independent variable values) for which the function is defined. It identifies all values that can be substituted into the function without causing any undefined operations, such as taking the square root of a negative number or dividing by zero.

Non-Negativity Constraint on Square Roots

The square root function is only defined for non-negative arguments in the realm of real numbers. This constraint means that whenever a square root is involved in a function, the expression inside the square root (the radicand) must be greater than or equal to zero. This is crucial in determining the domain of functions involving square roots.

Nested Radical Functions

Nested radical functions occur when a square root function contains another square root within its radicand. Evaluating the domain of such functions requires ensuring that both the inner and outer radicands satisfy the non-negativity condition. This typically involves solving inequalities for each radical sequentially to ensure all parts of the function are defined.

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