f colon left curly bracket $0$ comma $1$ right curly bracket to the power of $4$ rightwards arrow left curly bracket $0$ comma $1$ right curly bracket to the power of $4$ and $$f left parenthesis x right parenthesis$$is obtained by replacing the first bit of x with $1.$ For example, $$f left parenthesis $0100$ right parenthesis equals $1100.$

$$g colon left curly bracket $0$ comma $1$ right curly bracket to the power of $4$ rightwards arrow left curly bracket $0$ comma $1$ right curly bracket to the power of $4$ and $$g left parenthesis x right parenthesis$$is obtained by removing the first bit of x and placing the bit at the end. For example, $$g left parenthesis $1000$ right parenthesis equals $0001.$

Select the correct value for $$left parenthesis f ring operator g right parenthesis left parenthesis $0011$ right parenthesis$.$