Let $f:R\to R$and $g:R\to R$be two non-constant differentiable functions. If $f^{prime}\left(x\right)=\left(e^{\left(f\left(x\right)-g\left(x\right)\right)}\right)g^{prime}\left(x\right)$for all $x\in R$, and $f\left(1\right)=g\left(2\right)=1$, then which of the following statement(s) is (are) TRUE?$f\left(2\right)<1-{\left(\log \right)}_{e}2$(b) $f\left(2\right)>1-{\left(\log \right)}_{e}2$(c) $g\left(1\right)>1-{\left(\log \right)}_{e}2$(d) $g\left(1\right)<1-{\left(\log \right)}_{e}2$

Views: 1,199 students