Objective 3: Find the Inverse of a Function a. Show that f ( x ) = 2 x − 3 defines a one-to-one function. b. Write an equation for f − 1 ( x ) . c. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system .
Objective 3: Find the Inverse of a Function a. Show that f ( x ) = 2 x − 3 defines a one-to-one function. b. Write an equation for f − 1 ( x ) . c. Graph y = f ( x ) and y = f − 1 ( x ) on the same coordinate system .
Solution Summary: The author explains how the function f(x)=2x-3 defines a one to one function.
a. Show that
f
(
x
)
=
2
x
−
3
defines a one-to-one function.
b. Write an equation for
f
−
1
(
x
)
.
c. Graph
y
=
f
(
x
)
and
y
=
f
−
1
(
x
)
on the same coordinate system.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Chapter 4 Quiz 2 As always, show your work. 1) FindΘgivencscΘ=1.045.
2) Find Θ given sec Θ = 4.213.
3) Find Θ given cot Θ = 0.579. Solve the following three right triangles.
B
21.0
34.6° ca
52.5
4)c
26°
5)
A
b
6) B 84.0 a
42°
b
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY