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Chapter 2: Problem 2

Find the domain of each rational function. $$f(x)=\frac{7 x}{x-8}$$

Short Answer

Expert verified
The domain of \(f(x) = \frac{7x}{x-8}\) is all real numbers except \(x = 8\). Thus, the domain is \(x \ne 8\).

Step by step solution

01

Identify the Rational Function

The function given is \(f(x) = \frac{7x}{x-8}\). In the function, \(x\) is the variable, 7 is the coefficient of the \(x\) in the numerator and -8 is the coefficient of the \(x\) in the denominator.
02

Determine the denominator

For this function, the denominator is \(x-8\). A rational function is undefined when the denominator is equal to zero.
03

Solve for \(x\)

Solve the equation \(x-8 = 0\) for \(x\). Adding 8 to both sides of the equation gives \(x = 8\).
04

Define the Domain

The domain of \(f(x)\) is all real numbers except for \(x = 8\), because the function \(f(x)\) is undefined at \(x = 8\). Therefore, the domain is \(x \ne 8\).

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Most popular questions from this chapter

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}-x+1}{x-1}$$

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$g(x)=\frac{1}{(x+1)^{2}}$$

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