Question

Find the dicontinuities of the function. f(x) = x2 + 12x + 27 x2 + 4x + 3 . There is a removable discontinuity at (, ).

Answer 1

Answer:

Step-by-step explanation:

its -3 -3 for both

Answer 2

Solution-

$f(x)=\frac{x^{2}+12x+27 }{x^{2} +4x+3} =\frac{x^{2}+9x+3x+27 }{x^{2} +3x+x+3}=\frac{(x+3)(x+9)}{(x+3)(x+1)}$

Equating the denominator to 0,

⇒ (x+3)(x+1) = 0

⇒ x= -3, -1

∴ Discontinuities of the function f(x) is at -3, -1

As (x+3) is also a factor of the numerator, you will have what's called a removable discontinuity. That will show up as a hole in the graph.

∴ At x = -3, you will have removable discontinuity.