Find the Domain f(x)=(x-7)/(x+4)

Problem

ƒ(x)=(x−7)/(x+4)

Solution

1. Identify the condition for the domain of a rational function. A rational function is undefined when its denominator is equal to zero.

2. Set the denominator equal to zero to find the excluded values of x

x+4=0

3. Solve for x by subtracting 4 from both sides of the equation.

x=−4

4. State the domain as all real numbers except for the value that makes the denominator zero. In interval notation, this excludes −4

(−∞,−4)∪(−4,∞)

Final Answer

Domain:(−∞,−4)∪(−4,∞)

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