f:$\{0,1\}^4\backslash$rightarrow$\{0,1\}^4$ and f$($x$)$ is obtained by replacing the first bit of x with $1.$ For example, f$(0100)=1100.$

g:$\{0,1\}^4\backslash$rightarrow$\{0,1\}^4$ and g$($x$)$ is obtained by removing the first bit of x and placing a $0$ at the end. For example g$(0111)=1110.$

Select the function that is well$-$defined.

a$.$ g$\backslash$circ f

b$.$ f$\backslash$circ g

c$.$ g$^\{-1\}\backslash$circ g

d$.$ f$^\{-1\}\backslash$circ f