Let f(x) = log e (sin x), (0 < x < π) and g(x) = sin^–1 (e^–x), (x ≥ 0). If α is a positive real number such that a = (fog)'(α) and b = (fog)(α), then:

(A) a α ² + b α - a = -2 α ²

Limit, Continuity and Differentiability: JEE Main 2019 Mathematics question

JEE Main 2019 · 10 Apr, Evening shift · Q3658

JEE Main 201910 Apr, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let f(x) = log_e(sin x), (0 < x <

\pi

) and g(x) = sin^–1 (e^–x ), (x

\ge

0). If

\alpha

is a positive real number such that a = (fog)'(

\alpha

) and b = (fog)(

\alpha

), then :