Question

f(x) = ([x] + 1)/({x} + 1) for f: [0, 5/2) → (1/2, 3], where [ . ] represents greatest integer function and { . } represents fractional part of x , then which of the following is true. 

(A) f(x) is injective discontinuous function. 

(B) f(x) is surjective non-differentiable function. 

(C) min [lim_(x →1-)f(x), lim_(x →1+) f(x)] = f(1) 

(D) max (x values of point of discontinuity) = f(1)

Answer 1

Answer is (A), (B), (D)

Clearly, f(x) is discontinuous and bijective function (see Fig.).