{ EXAMPLE 1 The functions defined by the formulas { f(x) = √x and have domains D(f) = [0, ∞) and D(g) = (-∞0, 1]. The points common to these do- mains are the points [0, ∞) n(-∞, 1] = [0, 1]. The following table summarizes the formulas and domains for the various algebraic com- binations of the two functions. We also write f g for the product function fg. Function ƒ + g f-g g - f f.g f/g g/f Formula (f + g)(x) = √x + VI-x (f - g)(x) = √x - VT-x (8 - f)(x) = V1 -x - √x (f.g)(x) = f(x)g(x) = √x(1-x) f(x) //(x) tla R = g(x) = VT-x g(x) g(x) f(x) = HEL Domain [0, 1] = D(f) D(g) [0, 1] [0, 1] [0, 1] [0, 1) (x = 1 excluded) (0, 1] (x = 0 excluded) The graph of the function f + g is obtained from the graphs off and g by adding the corresponding y-coordinates f(x) and g(x) at each point x = D(f) nD(g), as in Figure 1.25. The graphs of f + g and f g from Example 1 are shown in Figure 1.26.
{ EXAMPLE 1 The functions defined by the formulas { f(x) = √x and have domains D(f) = [0, ∞) and D(g) = (-∞0, 1]. The points common to these do- mains are the points [0, ∞) n(-∞, 1] = [0, 1]. The following table summarizes the formulas and domains for the various algebraic com- binations of the two functions. We also write f g for the product function fg. Function ƒ + g f-g g - f f.g f/g g/f Formula (f + g)(x) = √x + VI-x (f - g)(x) = √x - VT-x (8 - f)(x) = V1 -x - √x (f.g)(x) = f(x)g(x) = √x(1-x) f(x) //(x) tla R = g(x) = VT-x g(x) g(x) f(x) = HEL Domain [0, 1] = D(f) D(g) [0, 1] [0, 1] [0, 1] [0, 1) (x = 1 excluded) (0, 1] (x = 0 excluded) The graph of the function f + g is obtained from the graphs off and g by adding the corresponding y-coordinates f(x) and g(x) at each point x = D(f) nD(g), as in Figure 1.25. The graphs of f + g and f g from Example 1 are shown in Figure 1.26.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![{
EXAMPLE 1
The functions defined by the formulas
{ f(x) = √x
and
g(x) = VT-x
have domains D(f) = [0, ∞) and D(g) = (-∞0, 1]. The points common to these do-
mains are the points
[0, ∞) n(-∞, 1] = [0, 1].
The following table summarizes the formulas and domains for the various algebraic com-
binations of the two functions. We also write f g for the product function fg.
Function
f + g
f-g
g - f
f.g
f/g
g/f
Formula
(f + g)(x) = √x + VI-x
(f - g)(x) = √x - VT-x
(g - f)(x) = V1 -x - √x
(f.g)(x) = f(x)g(x) = √x(1-x)
Vx
f(x)
X
//(x)
tla
Ⓡ
=
g(x)
8(x)
f(x)
Domain
[0, 1] = D(f) D(g)
[0, 1]
[0, 1]
[0, 1]
[0, 1) (x = 1 excluded)
(0, 1] (x = 0 excluded)
The graph of the function f + g is obtained from the graphs off and g by adding the
corresponding y-coordinates f(x) and g(x) at each point x = D(f) nD(g), as in Figure
1.25. The graphs of f + g and f g from Example 1 are shown in Figure 1.26.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77191d4e-5c44-442c-b3a4-67d14102d2c3%2F56004a2f-104d-40e5-bcb5-5845c5841321%2F9mdua7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:{
EXAMPLE 1
The functions defined by the formulas
{ f(x) = √x
and
g(x) = VT-x
have domains D(f) = [0, ∞) and D(g) = (-∞0, 1]. The points common to these do-
mains are the points
[0, ∞) n(-∞, 1] = [0, 1].
The following table summarizes the formulas and domains for the various algebraic com-
binations of the two functions. We also write f g for the product function fg.
Function
f + g
f-g
g - f
f.g
f/g
g/f
Formula
(f + g)(x) = √x + VI-x
(f - g)(x) = √x - VT-x
(g - f)(x) = V1 -x - √x
(f.g)(x) = f(x)g(x) = √x(1-x)
Vx
f(x)
X
//(x)
tla
Ⓡ
=
g(x)
8(x)
f(x)
Domain
[0, 1] = D(f) D(g)
[0, 1]
[0, 1]
[0, 1]
[0, 1) (x = 1 excluded)
(0, 1] (x = 0 excluded)
The graph of the function f + g is obtained from the graphs off and g by adding the
corresponding y-coordinates f(x) and g(x) at each point x = D(f) nD(g), as in Figure
1.25. The graphs of f + g and f g from Example 1 are shown in Figure 1.26.
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