Find the Domain h(x)=5/4x+3

Problem

h(x)=5/(4*x+3)

Solution

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

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

4*x+3=0

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

4*x=−3

4. Divide both sides by 4 to isolate x

x=−3/4

5. State the domain as all real numbers except for the value that makes the denominator zero.

Final Answer

Domain: *{x|x∈ℝ,x≠−3/4}

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