Respuesta :
Answer: Hence, the asymptotes of f(x) located at x=6 and x=-4.
Step-by-step explanation:
Since we have given that
[tex]f(x)= \frac{7}{x^2-2x-24}[/tex]
We need to find the asymptotes for the above function:
Asymptotes occur when denominator becomes zero.
[tex]x^2-2x-24=0\\\\x^2-6x+4x-24=0\\\\x(x-6)+4(x-6)=0\\\\(x-6)(x+4)=0\\\\x=6,-4[/tex]
Hence, the asymptotes of f(x) located at x=6 and x=-4.
f(x) = ∞, is not defined for x²- 2x - 24 = 0.
As the f(x) is not defined at -4 and 6.
The asymptotes of the hyperbola will be at x = -4 and 6.
What is the rectangular hyperbola?
A rectangular parabola is a hyperbola having three transverse axes and the conjugate axis of equal length. The arcs of a rectangular hyperbola are the same as the arc of the circle. The general equation of the rectangular hyperbola is x² + y² = a²
Given
[tex]\rm f(x) = \dfrac{7}{x^{2} -2x-24}[/tex] is a function.
To find
The asymptotes of a hyperbola.
f(x) = ∞, is not defined
x²- 2x - 24 = 0
x² - (6-4) x - 24 = 0
x² -6x + 4x -24 = 0
( x - 6 ) ( x + 4 ) = 0
As the f(x) is not defined at -4 and 6.
Thus the asymptotes will be at x = -4 and 6.
More about the rectangular hyperbola link is given below.
https://brainly.com/question/2791549
