jee-main 2015 Q71

jee-main · India · 10apr Composite & Inverse Functions Evaluate Composition from Algebraic Definitions

Let $f(x) = x^2$, $g(x) = \sin x$ for all $x \in \mathbb{R}$ and $h(x) = (gof)(x) = g(f(x))$. Statement I: $h$ is not differentiable at $x = 0$. Statement II: $(hog)(x) = \sin^2(\sin x)$. Which of the following is correct?
(1) Statement I is false, Statement II is true
(2) Statement I is true, Statement II is false
(3) Both Statement I and Statement II are true
(4) Both Statement I and Statement II are false

Let $f(x) = x^2$, $g(x) = \sin x$ for all $x \in \mathbb{R}$ and $h(x) = (gof)(x) = g(f(x))$. Statement I: $h$ is not differentiable at $x = 0$. Statement II: $(hog)(x) = \sin^2(\sin x)$.\\
Which of the following is correct?\\
(1) Statement I is false, Statement II is true\\
(2) Statement I is true, Statement II is false\\
(3) Both Statement I and Statement II are true\\
(4) Both Statement I and Statement II are false

Paper Questions

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