f:A B A = {0, 1, 2}, B = {0,1} f(0) = 1, f(1) = 0, f(2) = 1 1.Is f, as described above, a function? If it is not a function, explain why. 2.If f is a function. Answer the following: a.lsfinjective? If it is not injective, explain why. %3D %3D %3D b.lsf surjective? If it is not surjective, explain why. c.lsf bijective? If it is not bijective, explain why. d.Does f have an inverse? If f has an inverse, what is the domain and codomain of f-? If f does not have an inverse, explain why.
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- Question p . Consider the following functions: int min(int x, int y) { return x < y ? x : y; } int max(int x, int y) { return x < y ? y : x; } void incr(int *xp, int v) { *xp += v; } int square(int x) { return x*x; } Assume x equals 10 and y equals 100. The following code fragment calls these functions. int low = min(x,y); int high = max(x,y); for (i = low; i < high; incr(&i, 1)) t += square(i); The function min is called Answer times. The function max is called Answer times. The function incr is called Answer times. The function square is called Answer times. Full explain this question and text typing work only We should answer our question within 2 hours takes more time then we will reduce Rating Dont ignore this lineWrite a Racket function "combine" that takes two functions, f and g, as parameters and evaluates to a new function. Both f and g will be functions that take one parameter and evaluate to some result. The returned function should be the composition of the two functions with f applied first and g applied to f's result. For example (combine add1 sub1) should evaluate to a function equivalent to (define (h x) (sub1 (add1 x))). You will need to use a lambda function to achieve your result. Essentially you want (combine f g) to evaluate to a lambda function with f and g embedded inside. You can test your combine with invocations such as ((combine add1 add1) 1), which should evaluate to 3 since the anonymous function returned by combine is being applied to 1. Note: This is an example of a "function closure". f and g are defined in the scope of combine, but the lambda embeds a copy of them in the lambda function that can be used outside of combine's scope. When creating a lambda function in…It is good practice to plot the integrand function to check whether it is “well behaved” before you attempt to integrate. Singularities (i.e. x values where the f(x) tends towards minus or plus infinity) or other irregular behaviour (such as f(x) = sin( 1 x ) close to x = 0 are difficult to handle numerically. 1. Write a function with name plotquad which takes the same arguments as the quad command (i.e. f , a and b) and which • (i) creates a plot of the integrand f(x) and • (ii) computes the integral numerically using the quad function. The return values should be as for the quad function.
- ) Consider the following functions. Decide whether these functions are injective,surjective, and invertible. Justify your answer (e.g., if you claim that a function is invertible, you need togive a justification as to why you think that function is invertible). Give counterexamples when needed.You can draw arrow diagrams to help justifying your answer.a) Function f: ℤ × ℤ → ℤ is defined as f((a, b)) = 2b – 4a.b) A = {1, 2, 3}. Function f: ?(A) → {0, 1, 2, 3} is defined as f(X) = |X| where |X| = size of X. Forexample, |{1, 2}| = 2. ?(A) is the power set of A.c) Function f: {0, 1}3 → {0, 1}3 is defined by the following rule. For each string s ∈ {0, 1}3,f(s) = f(x1x2x3) = x3x1x2, where x1, x2, x3 ∈ {0, 1}. For example, if x1 = a, x2 = b, and x3 = c, thenf(abc) = cab. Another example: f(011) = 101.(6a) how many different functions f : A → B can be defined if m=3 and n=5? (6b) if m=4 and n=6 then how many different one-to-one functions f : A →B can be defined? (6c) if m=5 and n=4 then how many different onto functions f : A → B can be defined?Consider the following function. What is the purpose of the function f? Please do explain and describe in details all possible answers for this function given below.int f(int n) {if ((a >= b) && (c < b)) return b; else if (a >= b) return f(a, c, b); else return f(b, a, c);} To find the maximum number between a, b, and c. To find the middle number between a, b, and c. To find the minimum number between a, b, and c. None of the other statements.
- Consider the following function. What is the purpose of the function f? Please do explain and describe in details all possible answers for this function given below.int f(int n) {if ((a >= b) && (c < b)) return b; else if (a >= b) return f(a, c, b); else return f(b, a, c);} To find the maximum number between a, b, and c. To find the middle number between a, b, and c. To find the minimum number between a, b, and c. None of the other statements. Suppose the letters a,b,c,d,e,f have probabilities of 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a,b,c,d,e,f? Please show how is the Huffman tree, so that you can determine one of the options below. 0, 10, 110, 1110, 11110, 11111 11, 10, 01, 001, 0001, 0000 11, 10, 011, 010, 001, 000 110, 100, 010, 000, 001, 111 An adjacency matrix of a graph is given below:First, draw the graph defined by that adjacency matrix, and label the vertices of the graph with 1, 2,…In Dr-Racket, which of the following is not necessarily true of a function that takes no arguments? A) It can result in side effects B) It might return (void) C) It might return a value like any other function D) It has the same result every time it is called, since it has no input arguments to deal with E) It is called like any other function, i.e. inside parentheses F) It can result in both side effects and return valueQ14) Consider the definition of the function foo below. Assuming that the next function call to foo would pass the string "#1,2,3,4,5,6,7,8,9,10#" (without the quotes) to the parameter y, then which value would need to be passed to foo as the parameter x in order for the return value to be 3 0 1 2 3 4 5 6 7 8 9 10 None of these options
- Suppose we have g(n) = 2n and h(n) =n3 Below are a number of statements regarding how the functions grow depending on n and in relation to each other. Which of the above statements is true? A,B TRUE C,E TRUE A,D TRUE C TRUEI need help in this following mcq If the function fTwo() is called as shown below: int x = fTwo (5); What is the highest value the variable nRet will obtain throughout the function’s execution until right before returning the function’s result? 1 int fTwo(int nNum) 2 { 3 int i = 0, nRet = -1; 4 for(i = 2; i < nNum - 1; i++) 5 { 6 if(nNum == i * i) 7 nRet = i; 8 else if( (i - 1)*(i - 1) < nNum && nNum < i * i ) 9 nRet = i - 1; 10 } 11 return nRet; 12 } Group of answer choices A) zero B) 3 C) 2 D) 5Which functions are one-to-one? Which functions are onto? Describe the inversefunction for any bijective function.(a) f : Z → N where f is defined by f (x) = x4 + 1(b) f : N → N where f is defined by f (x) = { x/2 if x is even, x + 1 if x is odd}(c) f : N → N where f is defined by f (x) = { x + 1 if x is even, x − 1 if x is odd}