Find the Domain f(x)=1/2x-7

Problem

ƒ(x)=1/(2*x−7)

Solution

1. Identify the restriction for a rational function, which is that the denominator cannot be equal to zero.

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

2*x−7=0

3. Solve for x by adding 7 to both sides of the equation.

2*x=7

4. Divide both sides by 2 to isolate x

x=7/2

5. Determine the domain by excluding this value from the set of all real numbers.

Final Answer

Domain: *{x|x∈ℝ,x≠7/2}

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