f([x]) gives only integer outputs
False
f([x]) is the given function. Input to this function is x. immediately after getting x, it converts it into [x]. So f([x]) when x=1.5 will be f([1.5])=f(1). This value may or may not be an integer depending f(x). If f(x)=x2, then f(1) is not an integer. (f([x]) at x=1.5=f(1)=12=0.5). So the given statement is wrong.