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Chapter 1: Problem 27

Determine the domain of the function represented by the given equation. $$f(x)=3 x-4$$

Short Answer

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

Step by step solution

01

- Identify the function type

The function \(f(x)=3x-4\) is a linear function. It is represented by a straight line when graphed.
02

- Understand what constraints the domain

There are several situations that place constraints on the domain of a function - when the denominator of a fraction is zero, when you have an even root of a negative number, or when you have a logarithm of a negative number. In the given function \(f(x)=3x-4\), none of these situations occur.
03

- Determine the domain

Since the function is linear and there are no restrictions that would limit the domain, the domain of the function would be all real numbers.

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Most popular questions from this chapter

Suppose that \(h=-16 t^{2}+64 t+5 .\) Find two values of \(t\) for which \(h=53 .[1.1]\)

Sketch the graph of the piecewisedefined function. $$v(x)=\left\\{\begin{array}{ll} 2 x-2 & \text { if } x \neq 3 \\ 1 & \text { if } x=3 \end{array}\right.$$

The notation \(\left.f(x)\right|_{a} ^{b}\) is used to denote the difference \(f(b)-f(a) .\) That is, $$\left.f(x)\right|_{a} ^{b}=f(b)-f(a)$$ Evaluate \(\left.f(x)\right|_{0} ^{b}\) for the given function \(f\) and the indicated values of \(a\) and \(b\). $$f(x)=-3 x+2 ;\left.f(x)\right|_{4} ^{7}$$

Use interval notation to express the solution set of each inequality. $$|x-3|<10$$

Solve by completing the square or by using the quadratic formula. $$2 x^{2}+\sqrt{5} x-3=0$$
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