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Chapter 1: Problem 5

Find the domain of each function. $$f(x)=x^{2}-2 x-15$$

Short Answer

Expert verified
The domain of the function \(f(x) = x^{2} - 2x - 15\) is all real numbers.

Step by step solution

01

Step 1- Identify function type

Firstly, it is important to identify the type of function. Here \( f(x) = x^{2} - 2x - 15 \) is a quadratic function - a specific type of polynomial function.
02

- Identify the characteristics of the function type

A quadratic function, as well as other polynomial functions, are defined for all real numbers. This means there are no specific values of x that make the function undefined. There are no denominators that could become zero, no roots of negative numbers or logarithms of zero or negative numbers in the function.
03

- Conclude the domain

As there are no real values of x that make the function undefined, we can claim that the domain of the function is all real numbers.

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Most popular questions from this chapter

Suppose that \(h(x)=\frac{f(x)}{g(x)} .\) The function \(f\) can be even,odd, or neither. The same is true for the function \(g .\) a. Under what conditions is \(h\) definitely an even function? b. Under what conditions is \(h \quad\) definitely an odd function?

Will help you prepare for the material covered in the next section. Find the ordered pairs \((\quad, 0)\) and \((0, \quad)\) satisfying \(4 x-3 y-6=0\).

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\frac{1}{x}$$

In your own words, describe how to find the midpoint of a line segment if its endpoints are known.

If you are given a function's equation, how do you determine if the function is even, odd, or neither?
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