Domain of Square Root Function

MHB
Thread starter arl2267
Start date Nov 20, 2012
Tags

Domain Function

In summary, the domain of a function is the set of all possible input values for which the function is defined, also known as the independent variable or x-values. It is important to find the domain of a function to determine its range of output values and identify any restrictions or limitations on the input values. To find the domain, you need to consider the function's input values and any potential restrictions, such as division by zero or square roots of negative numbers. Common types of functions with restricted domains include rational, square root, and logarithmic functions. It is not possible for a function to have an empty or undefined domain, as it must have a defined set of input values to be considered a valid function.

Nov 20, 2012

arl2267

Find the domain of the function f(x)= (3x+5)^1/2.

Not quite sure how to even start this...

Last edited by a moderator: Nov 20, 2012

Mathematics news on Phys.org

Nov 20, 2012

MarkFL

Gold Member

MHB

Hint: To get a real value for the function, the radicand (expression under the radical) cannot be negative. So solve:

$\displaystyle 0\le3x+5$

Related to Domain of Square Root Function

1. What is the domain of a function?

The domain of a function is the set of all possible input values for which the function is defined. It is the independent variable or the x-values of a function.

2. Why is it important to find the domain of a function?

It is important to find the domain of a function in order to determine the range of values that the function can output. It also helps to identify any restrictions or limitations on the input values of the function.

3. How can you find the domain of a function?

To find the domain of a function, you need to look at the input values of the function and determine if there are any restrictions. Common restrictions include values that would result in division by zero or taking the square root of a negative number. You may also need to consider the type of function and its graph to identify any limitations on the input values.

4. What are some common types of functions with restricted domains?

Some common types of functions with restricted domains include rational functions (which have restrictions on the denominator), square root functions, and logarithmic functions.

5. Can a function have an empty or undefined domain?

No, a function must have a defined domain in order to be considered a valid function. A function with an empty domain means that there are no input values that can be used to produce an output, while a function with an undefined domain means that there are no restrictions on the input values.