Question

The range of the function f(x) = √(^{x2+ 4x}C_{2x² +  3}) is

(A)  {1, 2 √3}

(B)  {1, 2 √3, 3 √5 }

(C)   {1, 2, 3}

(D)   {1, 2}

Answer 1

Correct option  (A) {1, 2 √3}

Explanation :

For f(x) to be defined, we need to have

x² + 4x ≥ 0 ⇒ x ∈ (−∞, −4]∪[0, ∞]

 Also,

(x² + 4x) – (2x² + 3) ≥ 0 ⇒ x ∈ [1, 3]

However, nCr is defined only for the non-negative integral values of n and r and thus the domain is {1, 2, 3} and the range is {f(1), f(2), f(3)} = {1, 2 3}.