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Chapter 1: Problem 63

Find the domain of the function. $$g(x)=\frac{1}{x}-\frac{3}{x+2}$$

Short Answer

Expert verified
The domain of the function \(g(x)\) is all real numbers except \(x=0\) and \(x=-2\).

Step by step solution

01

Identify the Denominators

For this function, there are two fractions. The denominators for these fractions are 'x' and 'x+2'.
02

Solve for Undesirable Values

The function is undefined when the denominator is zero. So, identify the values of x that cause either denominator to be zero by solving the two equations \(x=0\) and \(x+2=0\). Solving these equations yields \(x=0\) for the first equation and \(x=-2\) for the second equation.
03

Exclude Undesirable Values

The domain of a function includes all the values that x can be except the undesirable values identified in Step 2. So, the domain of the function \(g(x)\) are all real values except \(x=0\) and \(x=-2\).

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Most popular questions from this chapter

Think About It Describe a type of function that is not one-to-one on any interval of its domain.

Proof Prove that if \(f\) is a one-to-one odd function, then \(f^{-1}\) is an odd function.

Find the domain of the function.$$f(x)=\sqrt[3]{16-x^{2}}$$.

Use the fact that the graph of \(y=f(x)\) has \(x\) -intercepts at \(x=2\) and \(x=-3\) to find the \(x\) -intercepts of the given graph. If not possible, state the reason.$$y=f(x-3)$$.

Evaluate the function at each specified value of the independent variable and simplify. \(f(x)=x \sqrt{x-3}\) (a) \(f(3)\) (b) \(f(12)\) (c) \(f(6)\)
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