Find the domain of the function

Question

Find the domain of the function. (Enter your answer using interval notation.)

g(x) =	x
7x2 + 6x − 1

 

 

Answer 1

g(x) = √(7x² + 6x - 1)

Domain = {x l 7x² + 6x - 1 ≥ 0}

(7x - 1)(x + 1) ≥ 0

7x - 1 = 0 when x = 1/7 and x + 1 = 0 when x = -1

when x < -1, (7x-1)(x+1) > 0

when -1 < x < 1/7, (7x-1)(x+1) < 0

when x > 1/7, (7x-1)(x+1) > 0

Domain (-∞, -1] ∪ [1/7, ∞)