Find the Domain f(x)=(8x+12)/(x^2+5x+4)

Problem

ƒ(x)=(8*x+12)/(x2+5*x+4)

Solution

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

x2+5*x+4≠0

2. Factor the quadratic expression in the denominator by finding two numbers that multiply to 4 and add to 5

(x+4)*(x+1)≠0

3. Solve for the excluded values of x by setting each factor to zero.

x+4=0⇒x=−4

x+1=0⇒x=−1

4. State the domain as all real numbers except for the values that make the denominator zero.

Domain={x|x∈ℝ,x≠−4,x≠−1}

Final Answer

Domain of *ƒ(x)=(−∞,−4)∪(−4,−1)∪(−1,∞)

Want more problems? Check here!