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Chapter 2: Problem 2

Find the domain of each function. $$f(x)=2(x+5)$$

Short Answer

Expert verified
The domain of the function is all real numbers.

Step by step solution

01

Identify the type of function

Firstly, we identify that \(f(x) = 2(x + 5)\) is a linear function, specifically, it's a simple multiplication and addition operation with the variable \(x\). We don't have any operations with \(x\) that could lead to undefined results, like division by zero or square root of a negative number.
02

Determine the domain

For linear functions, we are able to substitute any real number and still get a real number output, there are no constraints. Therefore, the domain is all real numbers.

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Most popular questions from this chapter

Explain how to determine whether a relation is a function. What is a function?

Simplify: \(2(x+h)^{2}+3(x+h)+5-\left(2 x^{2}+3 x+5\right)\)

graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. $$ \begin{aligned} x^{2}+y^{2} &=16 \\ x-y &=4 \end{aligned} $$

What is a relation? Describe what is meant by its domain and its range.

What is a piecewise function?
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