jee-advanced 2003 Q10

jee-advanced · India · mains Composite & Inverse Functions Symmetry, Periodicity, and Parity from Composition Conditions

If a function $\mathrm { f } : [ - 2 \mathrm { a } , 2 \mathrm { a } ] - - > \mathrm { R }$ is an odd function such that $\mathrm { f } ( \mathrm { x } ) = \mathrm { f } ( 2 \mathrm { a } - \mathrm { x } )$ for $\mathrm { x } \hat { \mathrm { I } } [ \mathrm { a } , 2 \mathrm { a } [$ and the left hand derivative at $\mathrm { x } = \mathrm { a }$ is 0 then find the left hand derivative at $\mathrm { x } = - \mathrm { a }$.

If $A = \left[ \begin{array} { l l } \alpha & 0 \\ 1 & 1 \end{array} \right]$ and $B = \left[ \begin{array} { l l } 1 & 0 \\ 5 & 1 \end{array} \right]$ are two matrices, then $A ^ { 2 } = B$ is true for

If a function $\mathrm { f } : [ - 2 \mathrm { a } , 2 \mathrm { a } ] - - > \mathrm { R }$ is an odd function such that $\mathrm { f } ( \mathrm { x } ) = \mathrm { f } ( 2 \mathrm { a } - \mathrm { x } )$ for $\mathrm { x } \hat { \mathrm { I } } [ \mathrm { a } , 2 \mathrm { a } [$ and the left hand derivative at $\mathrm { x } = \mathrm { a }$ is 0 then find the left hand derivative at $\mathrm { x } = - \mathrm { a }$.

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