Answer:
Option A
Step-by-step explanation:
From the piecewise function given in the picture,
f(x) = k³ + x If x < 3
= [tex]\frac{16}{k^2-x}[/tex] If x ≥ 3
Here, function is discontinuous at x = 3
If the function is continuous at x = 3 then,
k³ + 3 = [tex]\frac{16}{k^2-3}[/tex]
(k³ + 3)(k² - 3) = 16
k⁵ - 3k³ + 3k² - 9 = 16
k⁵ - 3k³ +3k² - 25 = 0
By using a graphing tool we can get the point where k = 2.081.
Option A is the answer.
