Find the Domain y=pi/x+kx

Problem

y=π/x+k*x

Solution

1. Identify the components of the function y=π/x+k*x

2. Analyze the term π/x to determine where it is undefined. A fraction is undefined when its denominator is equal to zero.

3. Set the denominator to zero to find the excluded value: x=0

4. Analyze the term k*x This is a linear term which is defined for all real numbers x

5. Combine the restrictions. The only value that makes the function undefined is x=0

6. Express the domain in interval notation or set-builder notation, representing all real numbers except zero.

Final Answer

Domain:{[x∈ℝ,x≠0]}

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