For what value(s) of k is the function f(x) continuous at x = -3 given #f(x) = -6x - 12# when x < -3, #f(x) = k^2 - 5k# when x = -3 and f(x) = 6 when x > -3?
There is no real value of
Looking at the first branch of the function we see that
Looking at the last branch, we see that
Because the left and right limits are both
#lim_(xrarr-3) f(x) = 6#.
Looking at the definition of
In order to make the function continuous at
If we are allowed imaginary solutions, we need
If we are restricted to real number solutions, then the proper answer is: there is no real value of