Suppose the utility functions $u(x_1,x_2)$ and $v(x_1,x_2)$ are related by $v(x_1,x_2)=f(u(x_1,x_2)).$ Which of the following cases are a positive monotonic transformation of $u(x_1,x_2)?[$Hint: If $f(u)$ is a positive monotonic transformation of $u,f^{\text{'}}(u)0]$

a$.f(u)=3\mathrm{.}14u$

b$.f(u)=5000-23u$

c$.f(u)=u-100$

d$.f(u)=lnu$

e$.f(u)=-e^{-u}$

f$.f(u)=\frac{1}{u}$

g$.f(u)=-\frac{1}{u}$