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Chapter 1: Problem 55

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

Short Answer

Expert verified
The domain of function \(g(x)=\frac{1}{x}-\frac{3}{x+2}\) is all real numbers except 0 and -2.

Step by step solution

01

Identify Potential Restrictions

Start by identifying values of x that would produce undefined results in the function. These would be values that set the denominator of either fraction to 0.
02

Set the Denominator of First Fraction Equal to Zero

By setting the denominator of the first fraction equal to zero, \(x=0\) is obtained. Therefore, x cannot be zero, because division by zero is undefined.
03

Set the Denominator of the Second Fraction Equal to Zero

Next, turn to the denominator of the second fraction. Set \(x+2 = 0\). Solving this gives \(x=-2\). Thus, \(x\) cannot be \(-2\), because again, division by zero is undefined.
04

Combine Restrictions

Finally, combine the restrictions from steps 2 and 3. The only two values that x cannot take on are 0 and -2. Therefore, the domain of the function is all real numbers except for 0 and -2.

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