Question

Find the domain of the function. $g(t)=\sqrt{3-t}-\sqrt{2+t}$

   Find the domain of the function.
$g(t)=\sqrt{3-t}-\sqrt{2+t}$

Calculus

James Stewart 7th Edition

Chapter 1, Problem 34

Instant Answer

Solved by Expert Nandini Singh

06/25/2019

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The expression inside a square root must be non-negative for the square root to be defined in the real number system. Show more…

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Find the domain of the function. $g(t)=\sqrt{3-t}-\sqrt{2+t}$

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Key Concepts

Domain of a Function

The domain of a function includes all input values for which the function is defined. It is vital in understanding functions because it indicates the range of acceptable values that can be substituted into the function without causing any undefined operations.

Square Root Function Restrictions

Square root functions require that the expression or radicand under the square root be nonnegative, as the square root of a negative number is not a real number. This restriction leads to setting up inequalities to ensure the radicand is greater than or equal to zero.

Solving Inequalities and Intersection of Conditions

When determining the domain of a function with multiple restrictions, each individual inequality must be solved separately. The overall domain of the function is then found by taking the intersection of these solution sets, ensuring all conditions are satisfied simultaneously.

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