4. For what value of the constant k the function
f(x)= x^ 2 -4 x-2 &if x ne2,\\ 2k - x &if x=2
is continuous at x = 2
A) -3
B) -1
C) 3
D) 1
We need to find the value of k such that the limit of f(x) as x approaches 2 from both sides is equal to f(2).
First, let's find the limit of f(x) as x approaches 2 from the left side:
lim x → 2- (x^2 - 4x - 2) = (2^2 - 4(2) - 2) = -6
Now, let's find the limit of f(x) as x approaches 2 from the right side:
lim x → 2+ (2k - x) = 2k - 2
For the function to be continuous at x = 2, these two limits must be equal. Therefore:
2k - 2 = -6
Solving for k, we get:
k = -2
Therefore, the answer is not one of the given choices.