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Chapter 1: Problem 31

Determine the domain of the function represented by the given equation. $$f(x)=\frac{4}{x+2}$$

Short Answer

Expert verified
The domain of the function is all real numbers except -2.

Step by step solution

01

Identify the Conditions for the Function to be Undefined

A rational function is undefined when the denominator is zero, because division by zero is undefined in mathematics. Therefore, for the function \(f(x) = \frac{4}{x + 2}\), we first need to find where the denominator is zero.
02

Solve for 'x'

To find when the denominator is zero, set the denominator equal to zero and solve for 'x'. In our case, we set \(x + 2 = 0\). Solving for this equation, we get \(x = -2\).
03

Finding the Domain

The domain of the function is all real numbers except for -2, because if we plug -2 into the function, the function would be undefined. Therefore, the domain of \(f(x) = \frac{4}{x + 2}\) is \(x \in R\), \(x \neq -2\).

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