Problem 2 [10pt] Implement the following three functions in hw3.rkt and submit your code to hw3-code Gradescope assignment. You may NOT use any of Scheme's imperative features (assignment/loops) or anything else not covered in class. You should use Racket (https://racket-lang.org) for your implementation. For all problems, you can assume all inputs obey the types as specified in a problem. a) (4pts) Define a function funpower in Racket. funpower takes in two arguments f (a function) and n (a non-negative integer), and returns a new function that applies f n times. For example (funpower sqrt 2) is a function that applies sqrt to input two times. ((funpower sqrt 2) 16) should evaluate to 2. #lang racket (define (double x) (* 2 x)) ; a helper function for testing code. (define (funpower fn) (lambda (x) x)) ((funpower sqrt 2) 16) ; should evaluate to 2 ((funpower double 0) 3) ; should evaluate to 3 Problem 2 [10pt] Implement the following three functions in hw3.rkt and submit your code to hw3-code Gradescope assignment. You may NOT use any of Scheme's imperative features (assignment/loops) or anything else not covered in class. You should use Racket (https://racket-lang.org) for your implementation. For all problems, you can assume all inputs obey the types as specified in a problem. a) (4pts) Define a function funpower in Racket. funpower takes in two arguments f (a function) and n (a non-negative integer), and returns a new function that applies f n times. For example (funpower sqrt 2) is a function that applies sqrt to input two times. ((funpower sqrt 2) 16) should evaluate to 2. #lang racket (define (double x) (* 2 x)) ; a helper function for testing code. (define (funpower fn) (lambda (x) x)) ((funpower sqrt 2) 16) ; should evaluate to 2 ((funpower double 0) 3) ; should evaluate to 3