contestada

Identify the domain of the given function: f(x) = (7x + 1) / (2x - 9)
a) (-[infinity], -1) ∪ (-1, [infinity])
b) (-[infinity], -1] ∪ [-1, [infinity])
c) (-[infinity], 0) ∪ (0, [infinity])
d) (-[infinity], [infinity])

Respuesta :

Rule: You cannot divide by zero.

Since zero cannot be in the denominator, the 2x-9 must be nonzero.

If it was zero, then...

2x-9 = 0

2x = 9

x = 9/2

x = 4.5

If x = 4.5, then the denominator is zero and causes a division by zero error.

We must kick this x value out of the domain. Poke a hole on the real number line at x = 4.5

We'll go from [tex](-\infty, \infty)[/tex] to [tex](-\infty, 4.5) \cup (4.5, \infty)[/tex]