jee-main 2023 Q77

jee-main · India · session1_29jan_shift1 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let $f : R \rightarrow R$ be a function such that $f ( x ) = \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 1 }$. Then
(1) $f ( x )$ is many-one in $( - \infty , - 1 )$
(2) $f ( x )$ is many-one in $( 1 , \infty )$
(3) $f ( x )$ is one-one in $[ 1 , \infty )$ but not in $( - \infty , \infty )$
(4) $f ( x )$ is one-one in $( - \infty , \infty )$

Let $f : R \rightarrow R$ be a function such that $f ( x ) = \frac { x ^ { 2 } + 2 x + 1 } { x ^ { 2 } + 1 }$. Then\\
(1) $f ( x )$ is many-one in $( - \infty , - 1 )$\\
(2) $f ( x )$ is many-one in $( 1 , \infty )$\\
(3) $f ( x )$ is one-one in $[ 1 , \infty )$ but not in $( - \infty , \infty )$\\
(4) $f ( x )$ is one-one in $( - \infty , \infty )$

Paper Questions

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