Question

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 f if exists.

Answer #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

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...

The system Px +Qy =R; Fx + Gy = H has solution(3,-1), where
F,G,H,P,Q, and R are nonzero real numbers.
Select all the systems that are also guaranteed to have the
solution (3,-1). (Select all that applies)
A. (P+F)x+(Q+G)y= R+H and Fx+Gy=H
B. (P+F)x+Qy= R+H and Fx+(G+Q)y=H
C.Px+Qy=R and (3P+F)x+(3Q+G)y=3H+R
D. Px+Qy=R and (F-2P)x+(G-2Q)y=H-2R
E. Px+Qy+R and 5Fx+ 5Gy

P=
1 0 0
0
.2 .3
.1 .4
.1
.2 .3 .4
0
0
0 1
(a) Identify any absorbing state(s).
(b) Rewrite P in the form:
I O
R Q
(c)Find the Fundamental Matrix, F.
(d)Find FR

A. Let p and r be
real numbers, with p < r. Using the axioms of
the real number system, prove there exists a real number q
so that p < q < r.
B. Let f: R→R be a polynomial
function of even degree and let A={f(x)|x
∈R} be the range of f. Define f
such that it has at least two terms.
1. Using the properties and
definitions of the real number system, and in particular the
definition...

1. Given the point P(5, 4, −2) and the point Q(−1, 2, 7) and
R(0, 3, 0) answer the following questions • What is the distance
between P and Q? • Determine the vectors P Q~ and P R~ ? • Find the
dot product between P Q~ and P R~ . • What is the angle between P
Q~ and P R~ ? • What is the projP R~ (P R~ )? • What is P Q~

How to solve this equation to find f(n), where
f(n)=1+p*f(n+1)+q*f(n-1). p,q are constant and p+q=1. We already
know two point f(0)=f(d)=0, d is a constant number.
what is f(n) as a function with p,q,d,n?

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

Suppose f(1) = −1, f(2) = 0, g(1) = 2, g(2) = 7, and f 0 (1) =
1, f0 (2) = 4, g0 (1) = 8, g0 (2) = −4.
(a) Suppose h(x) = f(x^2 g(x)). Find h 0 (1).
(b) Suppose j(x) = f(x) sin(x − 1). Find j 0 (1).
(c) Suppose m(x) = ln(x)+arctan(x) e x+g(2x) . Find m0 (1).

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 :...

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