Find the Domain (x^-1)/(4x^4)

Problem

(x(−1))/(4*x4)

Solution

1. Rewrite the expression using positive exponents to identify potential points of discontinuity.

(x(−1))/(4*x4)=1/(x⋅4*x4)

2. Simplify the denominator by applying the product rule for exponents.

1/(4*x5)

3. Identify the restriction by setting the denominator equal to zero, as division by zero is undefined.

4*x5=0

4. Solve for x to find the value that must be excluded from the domain.

x5=0

x=0

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

Domain={x|x≠0}

Final Answer

Domain of (x(−1))/(4*x4)=(−∞,0)∪(0,∞)

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