Find the Domain (5x^2+4)/(2x^2-7)

Problem

ƒ(x)=(5*x2+4)/(2*x2−7)

Solution

1. Identify the condition for the domain of a rational function, which requires that the denominator cannot be equal to zero.

2*x2−7≠0

2. Isolate the x2 term by adding 7 to both sides of the equation.

2*x2≠7

3. Divide both sides by 2 to solve for x2

x2≠7/2

4. Solve for x by taking the square root of both sides, remembering to include both the positive and negative roots.

x≠±√(,7/2)

5. Rationalize the denominator to express the excluded values in simplest form.

x≠±√(,14)/2

6. State the domain in interval notation, excluding the values where the denominator is zero.

(−∞,−√(,14)/2)∪(−√(,14)/2,√(,14)/2)∪(√(,14)/2,∞)

Final Answer

Domain:(−∞,−√(,14)/2)∪(−√(,14)/2,√(,14)/2)∪(√(,14)/2,∞)

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