Question

f (x) = x + √x²  is  a function from R → R, then f (x) is

(A) Injective

(B) Surjective

(C) Bijective

(D) None of these

Answer 1

Correct option (D) None of these

Explanation :

We have

f (x) = x + √x² = x + |x|

 Now, f is not one-to-one as 

f (-1)  = f(-2) = 0

But −1 ≠ 2 and also f is not onto since f (x) ≥ 0,∀ x ∈ R Also, the range of f is  (0, ∞) ⊂ R .