Determine the Domain: Analyzing the Function 10x Divided by 1/2

Question

Look at the following function:

$\frac{10x}{\frac{1}{2}}$

What is the domain of the function?

Video Solution

Solution Steps

00:00 Does the function have a domain? And if so, what is it?

00:03 To find the domain, remember that division by 0 is not allowed

00:07 The denominator is a constant number different from 0

00:10 Therefore there is no domain restriction

00:13 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Simplify the expression.

Given the function:

$f(x) = \frac{10x}{\frac{1}{2}}$

We can simplify this expression by multiplying by the reciprocal of the denominator:

$f(x) = 10x \times 2 = 20x$

Step 2: Determine the domain.

Since $f(x) = 20x$ is a linear function, it is defined for all real numbers. There are no restrictions on $x$ since no division by zero or any undefined operations are present.

Conclusion: The domain of the function is all real numbers. This corresponds to choice :

All real numbers

Therefore, the domain of the function is all real numbers.

Answer

All real numbers

Related Subjects

Domain of a Function Indefinite integral Inputing Values into a Function

Question Types

Domain of a Function: Find the domain of an expression with fractions