I got B

But the ans says D

Since k can have 2 values

One is -1 and other is between 0 to 1 (which is 0.414)

Although the question says all integer values of x

I hope someone can explain

The only possible explanation I can think of is that we don’t know the value of f(k) when k is a non-integer. As in:

f(k) = x^2 + 2^k, when k is integer and

f(k) = ?, when k is not an integer

What is the source of this question?