jee-main 2024 Q71

jee-main · India · session2_05apr_shift2 Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification

Let $f , g : \mathbf { R } \rightarrow \mathbf { R }$ be defined as : $f ( x ) = | x - 1 |$ and $g ( x ) = \begin{cases} \mathrm { e } ^ { x } , & x \geq 0 \\ x + 1 , & x \leq 0 \end{cases}$ Then the function $f ( g ( x ) )$ is
(1) neither one-one nor onto.
(2) one-one but not onto.
(3) onto but not one-one.
(4) both one-one and onto.

Let $f , g : \mathbf { R } \rightarrow \mathbf { R }$ be defined as : $f ( x ) = | x - 1 |$ and $g ( x ) = \begin{cases} \mathrm { e } ^ { x } , & x \geq 0 \\ x + 1 , & x \leq 0 \end{cases}$ Then the function $f ( g ( x ) )$ is\\
(1) neither one-one nor onto.\\
(2) one-one but not onto.\\
(3) onto but not one-one.\\
(4) both one-one and onto.

Paper Questions

Q61 Q62 Q63 Q64 Q65 Q66 Q67 Q68 Q69 Q70 Q71 Q72 Q73 Q74 Q75 Q76 Q77 Q78 Q79 Q80 Q81 Q82 Q83 Q84 Q85 Q86 Q87 Q88 Q89 Q90