The function below is defined for all x except one value of x. if possible, define f(x) at the exceptional point in a way continuous for all x. f(x) = x^2 - 13x + 22/x-11, x notequalto 11

F(x=11)= (-31)

Step-by-step explanation:

for the function

F(x) = x² - 13*x + 22/x-11 , for x ≠ 11

then in order to define F(x=11) so  F is continuous (see Note below) . By definition of continuity of a function:

F(x) is continuous in x=11 if lim F(x)=F(a) when x→a

then

when x→a , lim x² - 13x + 22/x-11 = lim 11² - 13*11 + 22/11 -11 = -3*11 + 2 = -31 = F(x=11)

then

F(x=11)= (-31)

Note:

F is not continuous in all x since

when x→0⁺ ,  lim (0⁺) ² - 13*0⁺  + 22/0⁺ -11 = (+∞)

when x→0⁻,  lim (0⁻) ² - 13*0⁻  + 22/0⁻ -11 = (-∞)

then

limit F(x) , when x→0 does not exist since the limit from the left and from the right do not converge → since the limit does not exist , the function is not continuous  in x=0