JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

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Analyzing +4 | -1

Let

f(x) = {\log _e}(\sin x),(0 < x < \pi )

and

g(x) = {\sin ^{ - 1}}({e^{ - x}}),(x \ge 0)

. If

\alpha

is positive real number
such that

a = (fog)'(\alpha )

and

b = (fog)(\alpha )

, then

View answer and explanation

Correct option: B

a{\alpha ^2} - b\alpha - a = 1

Option B (

a{\alpha ^2} - b\alpha - a = 1

) is correct because the given functions are composed and simplified, then differentiated and evaluated at

\alpha

to satisfy the equation.

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