Question

_{Determine which of the following functions are one to one
and explain your reasoning.}

1. f(x)=
x^{2}-3x-10

2. g(x)=
-2x^{3}+1

Answer #1

Determine which of the following functions are injective
(one-to-one) on their respective domains and codomains
(a) f : ℝ → [0,∞), where f(x) = x²
(b) g : ℕ → ℕ, where g(x) = 3x − 2
(c) h : ℤ_7 → ℤ_7, where h(x) ≡ 5x + 2 (mod 7)
(d) p : ℕ ⋃ {0} → ℕ ⋃ {0}, where p(x) = x div 3

Determine which of the following functions are injective,
surjective, bijective (bijectivejust means both injective and
surjective).
(a)f:Z−→Z, f(n) =n2.
(d)f:R−→R, f(x) = 3x+ 1.
(e)f:Z−→Z, f(x) = 3x+ 1.
(g)f:Z−→Zdefined byf(x) = x^2 if x is even and (x −1)/2 if x is
odd.

1) Determine whether x3 is O(g(x)) for the following:
a. g(x) = x2 + x3
b. g(x) = x2 + x4
c. g(x) = x3 / 2 2)
Show that each of these pairs of functions are of the same
order:
a. 3x + 7, x
b. 2x2 + x - 7, x2

Determine the intervals on which the following functions are
increasing and decreasing.
a) f(x) = 12 + x - x^2
b) g(x) = 2x^5 - (15x^4/4) + (5x^3/3)

1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
(e) j(x) = ln(x) / x5
(f) k(x) = ln(cot(x))
(g) L(x) = 4 csc^-1 (x2)
(h) m(x) = sin(x) / cosh(x)
(i) n(x) = 2 tanh^-1 (x4 + 1)

Use the cancellation equations to show that the following
functions f and g are inverses of one another f(x)= x-5/2x+3 g(x)=
3x+5/1-2x please explain

Determine which of the following equations are well defined
functions with an independent variable x. Explain.
A. 2y / x^2 - 3|x| = 1
B. Y^2 + x^2 = 10

Given the functions: f(x) = 6x+9 and g(x) =7x-4, determine each of
the following. Give your answers as simplified expressions written
in descending order.
(F+g)(x)=
(F-g)(x)=
(F•g)(x)=
(F/g)(x)=

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...

determine whether each of the following functions are one-to-one
by using the horizontal line test.
(a) f(x) = x2 + 5
Yes, it is one-to-one. No, it is not
one-to-one.
(b) g(x) = 3x3 + 2
Yes, it is one-to-one.No, it is not
one-to-one.
(c) h(x) = |x - 2|
Yes, it is one-to-one.No, it is not
one-to-one.

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