The inverse of the function f x = log a x + x 2 + 1 (where, a < 0 , a ≠ 1 ) is

Step-by-step solution

Let f x = y , then a y = x + x 2 + 1 ⇒ a - y = 1 x + x 2 + 1 ⇒ a - y = x - x 2 + 1 - 1 [rationalising] ∴   a y - a - y = 2 x ⇒ x = 1 2 a y - a - y ∴   f - 1 y = 1 2 a y - a - y ∵   f x = y ⇒ x = f - 1 y ⇒ f - 1 x = 1 2 a x - a - x [replacing y by x ] Hence, option (a) is correct.