Let $M$ be a Turing Machine Transducer that computes the function

$f$:$DR$ where $D=\{a^n$:$n1)$ and $R=\{a,b{\}}^{+}.$

a$.$ Give an instantaneous trace of $M$ when the input is $w=a.$ What is the

output of $f(a)?$

b$.$ Give a simple description of the function $f$ that is computed by M$.$ Justify

your answer.