Question

Find the domain of the function. $$f(x)=\frac{3}{\sqrt{x-4}}$$

   Find the domain of the function.
$$f(x)=\frac{3}{\sqrt{x-4}}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 69

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

The function is given by \( f(x) = \frac{3}{\sqrt{x-4}} \). The expression inside the square root is \( x - 4 \). Show more…

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Find the domain of the function. $$f(x)=\frac{3}{\sqrt{x-4}}$$

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Key Concepts

Solving Inequalities for Domain

To find the valid domain of a function, one must often solve inequalities that arise from the restrictions imposed by the function, such as those from square roots (non-negative conditions) and denominators (non-zero conditions). This process combines and simplifies the said conditions to identify all acceptable input values.

Restriction on Denominator

Any expression that appears in the denominator of a function must not equal zero, as division by zero is undefined. This requirement adds another layer of restrictions on the domain, ensuring the function does not involve any undefined operations.

Square Root Function

Square root functions require that the expression inside the square root (the radicand) is non-negative, because the square root of a negative number is not a real number. This property sets a primary restriction on the domain when square roots are involved.

Domain of a Function

The domain of a function is the set of all input values for which the function is defined. It takes into account any restrictions imposed by the operations within the function, such as square roots, denominators, logarithms, etc.

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