jee-main 2022 Q71

jee-main · India · session1_26jun_shift2 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined as $f ( x ) = x - 1$ and $g : R \rightarrow \{ 1 , - 1 \} \rightarrow \mathbb { R }$ be defined as $g ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 1 }$. Then the function $f o g$ is:
(1) One-one but not onto
(2) onto but not one-one
(3) Both one-one and onto
(4) Neither one-one nor onto

Let $f : \mathbb { R } \rightarrow \mathbb { R }$ be defined as $f ( x ) = x - 1$ and $g : R \rightarrow \{ 1 , - 1 \} \rightarrow \mathbb { R }$ be defined as $g ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 1 }$. Then the function $f o g$ is:\\
(1) One-one but not onto\\
(2) onto but not one-one\\
(3) Both one-one and onto\\
(4) Neither one-one nor onto

Paper Questions

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