JEE PYQ: Functions Question 29
Question 29 - 2019 (10 Apr Shift 2)
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 $a = (f \circ g)’(\alpha)$ and $b = (f \circ g)(\alpha)$, then:
(1) $a\alpha^2 + b\alpha + a = 0$
(2) $a\alpha^2 - b\alpha - a = 1$
(3) $a\alpha^2 - b\alpha - a = 0$
(4) $a\alpha^2 + b\alpha - a = -2a^2$
Type: MCQ
Show Answer
Answer: (2) $a\alpha^2 - b\alpha - a = 1$
Solution
$f(g(x)) = -x$, so $b = -\alpha$, $a = -1$
$a\alpha^2 - b\alpha - a = -\alpha^2 + \alpha^2 + 1 = 1$
BETA
