JEE Main 20241 Feb, Morning shiftMathematicsHardSets, Relations and Functions168× since 2002Let f:R→Rf: \mathbf{R} \rightarrow \mathbf{R}f:R→R and g:R→Rg: \mathbf{R} \rightarrow \mathbf{R}g:R→R be defined as f(x)={logex,x>0e−x,x≤0f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.f(x)={logex,e−x,x>0x≤0 and g(x)={x,x⩾0ex,x<0g(x)=\left\{\begin{array}{ll}x, & x \geqslant 0 \\ \mathrm{e}^x, & x<0\end{array}\right.g(x)={x,ex,x⩾0x<0. Then, gof : R→R\mathbf{R} \rightarrow \mathbf{R}R→R is :AOption A. one-one but not ontoBOption B. neither one-one nor ontoCOption C. onto but not one-oneDOption D. both one-one and ontoCheckSkip · show solution
