Question

Let f(x)=(x+8)/(4x^(2)-25)=((x+8))/((2x+5)(2x-5)) The domain of the function in interval notation is:

Answer 1

The domain of the function is (-∞, -5/2) ∪ (-5/2, 5/2) ∪ (5/2, ∞).

Step-by-step explanation:

The domain of the function can be determined by finding the values of x that would make the denominator equal to zero. In this case, the denominator is (2x+5)(2x-5), so we set each factor equal to zero and solve for x:

• For 2x+5=0, x=-5/2.
• For 2x-5=0, x=5/2.

Since the denominator cannot be zero, the domain of the function is all real numbers except x=-5/2 and x=5/2. In interval notation, the domain is (-∞, -5/2) ∪ (-5/2, 5/2) ∪ (5/2, ∞).