Find the Domain g(x)=3/4x+2

Problem

g(x)=3/(4*x+2)

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 values that must be excluded from the domain.

4*x+2=0

3. Solve for x by subtracting 2 from both sides.

4*x=−2

4. Divide both sides by 4 to isolate x

x=−2/4

5. Simplify the fraction.

x=−1/2

6. State the domain. The domain consists of all real numbers except x=−1/2

Final Answer

Domain: *{[x∈ℝ,x≠−1/2]}

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