Question 1 (10 points) Which of the following functions is not an onto function? f: R...
For each of the following functions, state whether or not the function is one-to-one, onto, both, or neither: 1) f : Z → Z defined by f(x)=2x + 1; 2) f : R → R defined by f(x)=2x + 1;
7. Determine whether each of these functions is one-to-one or onto. (a) f:Z + Z, f(n) 3n +1.
3. (10 points) Let F denote the vector space of functions f: R + R over the field R. Consider the functions fi, f2. f3 E F given by f1(x) = 24/3, f2() = 2x In(9), f() = 37*+42 Determine whether {f1, f2, f3} is linearly dependent or linearly independent, and provide a proof of your answer.
3. Which of the following functions are onto (surjective)? Mark them with a (a) f: (0, 0o) -R given by f(x) In r (b) f: , R given by f(x) tan r (c) f: (0, oo) -R given by f(x)-2 (d) f: R -(0, 00) given by f(x) 2 2' 2
1. Consider the function R R defined by tz) 3+ a. Prove that onto. See Examples 227 2.29 and review the definition of conta X Y is onto if (V) ve (entre X T HS is one to one, and is a one-to-one respondence. Find the f ull b. It can also be shown that Ser Example 2.32. and R ) 2. Consider the functions : Z Q and defined to go State the domain and range of the function...
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Determine whether the rule describe a function with the given domain and target. You must provide a specific counterexample if you determine it is not a function. (Note that the symbol squareroot refers to the principal or positive square squreroot .) f:R rightarrow R where f(x) = sqaurerootx f:Z rightarrow where f(n) = squaretrootn^2 + 1 For c, d and e below, consider the function: f: {0,1}^n rightarrowZ (i.e., f maps elements from the set of all bit strings...
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
2) (12) f:R-(3/2)-R-10, (x) 1/(3 2x) g:R--21->R-1o), g (x)1/ (x 2) h:R-(-4/3]-R-(1/3), h(x) (f o g) (x) Verify if h(x) is one to one and onto. If it is, find the inverse function of h(x).
2. (10 points) Given the following functions: f()= r* - 50x3 +1, g(x) = 24 Show that f(x) = N(g(2) using the definition of 10. Do not forget to provide the witnesses.
Python 1. Open up IDLE and in a multiline comment write “Functions and Sets II,” your name, and the date. 2. Use Python to write a function f(n) that finds the sum of the first n positive integers. Do not use the sum() function or lists. Write the function from scratch. Then use a for loop to print the sums for n = 10, 50, 1000. 3. Finding the Image of a function Suppose that we have a function f...
Question 12 (5 points) Consider the function f(x) = x2. Which of the following functions shifts f(x) downward 5 units and to the right 3 units? OA A) f(x) = (x + 3)2 - 5 B) f(x) = (x - 3)2 - 5 C) f(x) = (x - 5)2 + 3 OD) f(x) = (x - 5)2 - 3