Find the Domain f(x)=(3x)/(x+5)

Problem

ƒ(x)=(3*x)/(x+5)

Solution

1. Identify the type of function. This is a rational function, which is defined for all real numbers except where the denominator is equal to zero.

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

x+5=0

3. Solve for x by subtracting 5 from both sides of the equation.

x=−5

4. Determine the domain by excluding the value that makes the denominator zero. The domain consists of all real numbers except x=−5

5. Express the domain in interval notation.

(−∞,−5)∪(−5,∞)

Final Answer

Domain: *(−∞,−5)∪(−5,∞)

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