# 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?

##### 1 Answer

There is no real value of

#### Explanation:

Function

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# .

To make

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