Determine the domain of the function f(x) = x^2 + 6x +5/x^2 - 25 a. (-1, 5) b. (5, 5) c. (-infinity, -1) U (-1,5) U (5, infinity) d. (-infinity, -5) U (-5, 5) U (5, infinity)

Question

asked Jan 10, 2020 168k views

2 Answers

Nope · Answer 1 · 2020-01-14T23:05:29+0000

Answer:

The answer to your question is the last option

Explanation:

Here there is a rational function so, we need to find the values where the denominator equals zero.

f(x) = (x^(2) + 6x + 5)/(x^(2)- 25 )

x^(2) - 25 = 0

Factor (x - 5)(x + 5) = 0

x₁ - 5 = 0 x₂ + 5 = 0

The function does not exist in -5 and 5

x₁ = 5 x₂ = -5

Domain

( -∞ , -5) U (-5, 5) U (5, ∞)