Find the Domain (6-2)/(8+5x-1)

Problem

ƒ(x)=(6−2)/(8+5*x−1)

Solution

1. Simplify the expression to identify the denominator more clearly.

ƒ(x)=4/(5*x+7)

2. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

5*x+7≠0

3. Solve the inequality for x by subtracting 7 from both sides.

5*x≠−7

4. Divide both sides by 5 to isolate x

x≠−7/5

5. Express the domain in interval notation, representing all real numbers except −7/5

(−∞,−7/5)∪(−7/5,∞)

Final Answer

Domain:(−∞,−7/5)∪(−7/5,∞)

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