Let and . If the set of real values of 'a' for which is , then find the value of .…

MATHEMATICS · Subjective · CBSE · Mathematics · Inverse Trigonometric Functions · Inverse Trigonometric Functions

Problem

Let

f(x) = x^2 - 2ax + a - 2

and

g(x) = \left[ 2 + \sin^{-1} \frac{2x}{1+x^2} \right]

. If the set of real values of 'a' for which

f(g(x)) < 0, \forall x \in R

(k_1, k_2)

, then find the value of

(10k_1 - 3k_2)

. [Note :

[k]

denotes greatest integer less than or equal to

k