Question

Prob 5: i) Suppose f: R → Z where ?(?) =[2? - 1] a. If A...

Prob 5:
i) Suppose f: R → Z where ?(?) =[2? - 1]
a. If A = {x | 1 =< x =< 4}, find f(A).
b. If C = {-9, -8}, find f−1(C).
c. If D = {0.4, 0.5, 0.6}, find f−1(D).
(ii) Suppose g: A → B and f: B → C where A = {a, b, c, d}, B = {1, 2, 3}, C = {2, 3, 6, 8}, and g and f
are defined as g = {(a, 2), (b, 1), (c, 3), (d, 2)} and f = {(1, 8), (2, 3), (3, 2)}.
a. Find f ∘ g.

Please show all steps

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
1. A function f : Z → Z is defined by f(n) = 3n − 9....
1. A function f : Z → Z is defined by f(n) = 3n − 9. (a) Determine f(C), where C is the set of odd integers. (b) Determine f^−1 (D), where D = {6k : k ∈ Z}. 2. Two functions f : Z → Z and g : Z → Z are defined by f(n) = 2n^ 2+1 and g(n) = 1 − 2n. Find a formula for the function f ◦ g. 3. A function f :...
Suppose g: P → Q and f: Q → R where P = {1, 2, 3,...
Suppose g: P → Q and f: Q → R where P = {1, 2, 3, 4}, Q = {a, b, c}, R = {2, 7, 10}, and f and g are defined by f = {(a, 10), (b, 7), (c, 2)} and g = {(1, b), (2, a), (3, a), (4, b)}. (a) Is Function f and g invertible? If yes find f −1 and    g −1 or if not why? (b) Find f o g and g o...
Let f : R → R + be defined by the formula f(x) = 10^2−x ....
Let f : R → R + be defined by the formula f(x) = 10^2−x . Show that f is injective and surjective, and find the formula for f −1 (x). Suppose f : A → B and g : B → A. Prove that if f is injective and f ◦ g = iB, then g = f −1 .
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2)....
5. Part I If f(x) = 2x 2 - 3x + 1, find f(3) - f(2). A. 0 B. 7 C. 17 Part II If G( x ) = 5 x - 2, find G-1(x). A. -5x + 2 B. (x + 2)/5 C. (x/5) + 2 Please help me solve this problem and if you can please also show or explain how you got that answer. Thank you! :)
For functions f and g, where f(x) = 1 + x 2 , g(x) = x...
For functions f and g, where f(x) = 1 + x 2 , g(x) = x − 1 in C[0, 1] with the inner product defined by the integral: hf , gi = Z 1 0 f(x)g(x)dx, (a) find the norm of f and g. (b) find unit vectors in the directions of f and g. (c) find the cosine of the angle θ between f and g. (d) find the orthogonal projection of f along g
Suppose g : A → B and f : B → C where A = {1,...
Suppose g : A → B and f : B → C where A = {1, 2, 3, 4} B = {a, b, c} C = {3, 5, 7} and f and g are defined by g = {(1, c), (2, a), (3, b), (4, a)} f = {(a, 5), (b, 7), (c, 3)}. a. Find f∘g b. Find f-1
Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f...
Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f : R 2 =⇒ R 2 with f(z) =z1.x + z2.y for any z = [z1, z2] T ∈ R 2 . Further, z = g(r) = [r 2 , r3 ] where r ∈ R . Show how chain rule is applied here giving major steps of the calculation, write down the expression for ∂f ∂r , and also evaluate ∂f/ ∂r at...
Suppose z is implicitly implicitly defined by the equation: F(x, y, z) = 4x^ −1 −...
Suppose z is implicitly implicitly defined by the equation: F(x, y, z) = 4x^ −1 − 3x 3 yz + e^ z/ (x − 2) = c where c is a constant. Compute the first and second order partial derivatives of z with respect to x and y
Show (-1,1)~R (where R= set of real numbers) by f(x)= x/(1-|x|) Use this to show g(x)=x/(d-|x|)...
Show (-1,1)~R (where R= set of real numbers) by f(x)= x/(1-|x|) Use this to show g(x)=x/(d-|x|) is also a bijection (i.e. g: (-d,d)->R) Finally consider h(x)= x + (a+b)/2 and show it is a bijection where h: (-d,d)->(a,b) Conclude: R~(a,b)
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine...
3. For each of the piecewise-defined functions f, (i) determine whether f is 1-1; (ii) determine whether f is onto. Prove your answers. (a) f : R → R by f(x) = x^2 if x ≥ 0, 2x if x < 0. (b) f : Z → Z by f(n) = n + 1 if n is even, 2n if n is odd.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT