cmi-entrance 2014 QA3

cmi-entrance · India · ugmath 3 marks Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Given a real number $x$, define $g ( x ) = x ^ { 2 } e ^ { x }$ if $x \geq 0$ and $g ( x ) = x e ^ { - x }$ if $x < 0$.
(A) The function $g$ is continuous everywhere.
(B) The function $g$ is differentiable everywhere.
(C) The function $g$ is one-to-one.
(D) The range of $g$ is the set of all real numbers.

Given a real number $x$, define $g ( x ) = x ^ { 2 } e ^ { x }$ if $x \geq 0$ and $g ( x ) = x e ^ { - x }$ if $x < 0$.\\
(A) The function $g$ is continuous everywhere.\\
(B) The function $g$ is differentiable everywhere.\\
(C) The function $g$ is one-to-one.\\
(D) The range of $g$ is the set of all real numbers.

Paper Questions

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