1 Find the inverse of each of the following functions. f: x 6x + 5, x ER x +4 5 a b f:x→ cf: x4-2x, x = R 2x + 7 d f:x→ 3 e f i , ER f: x2x³ +5, x € R 1 f: xH +4, ER and x 0. x f: x→ 5 -, ER g f:x→ x-1 h f: x (x + 2)² + 7, x = Rand x > -2 3 (2x 3)² -5, x R and x > 2 *, €Randr #1 j f: x x² - 6x, x = R and x > 3 2 A function is called self-inverse if f(x) = f(x) for all x in the domain. Show that the following functions are self-inverse. a f: x5-x, x ER b f:xx, x ER c f:x+ 4 -, ER anda #0 x
1 Find the inverse of each of the following functions. f: x 6x + 5, x ER x +4 5 a b f:x→ cf: x4-2x, x = R 2x + 7 d f:x→ 3 e f i , ER f: x2x³ +5, x € R 1 f: xH +4, ER and x 0. x f: x→ 5 -, ER g f:x→ x-1 h f: x (x + 2)² + 7, x = Rand x > -2 3 (2x 3)² -5, x R and x > 2 *, €Randr #1 j f: x x² - 6x, x = R and x > 3 2 A function is called self-inverse if f(x) = f(x) for all x in the domain. Show that the following functions are self-inverse. a f: x5-x, x ER b f:xx, x ER c f:x+ 4 -, ER anda #0 x
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Please answer 1.A, 1.E, 1.J and 2.E
Transcribed Image Text:1:45 PM Fri Nov 25
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AA
S 2.3 Inverse Functions | Schoology
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e
f
h
i
t: x→
g f:x→
с
f:
: xH
HI
3
f : x → 2x³ +5, x € R
1
a
d f f: x→
X
f: x→
f f: x→
5
X 1
bf f: x →
f:
:
x → (x + 2)² + 7, x = R and x
j
f:x →x² - 6x, x = Randx ≥ 3
2 A function is called self-inverse if f(x)
following functions are self-inverse.
a f:x → 5-x,x ≤ R
b f:x⇒ −x,x = R
4
f:x→ -,x ER and x 0
X
+ 4,¤ ¤ R and x ‡0
f:
: x → (2x − 3)² – 5, x ≤ Rand x
6
X
-, x ER
5x'
x + 5
3 Find the inverse
f: x →
‚ x ≤ Randx ‡ 1
"
X
csusa-fl.schoology.com
x ER and x = 0
x - 1
3x 1
S Schoology
2
2x 3
x = R and x 1
"
X - - 2
2x + 1
X 4
x = R and x ‡
‚x € R andx ‡ 2
9
=
3
2
of each of the following functions.
x = R and x ‡ 4
9
3
2
f¹(x) for all x in the domain. Show that the
+
b My Questions | bartleby
ab】 ↓
50%
![1:45 PM Fri Nov 25
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a
1 Find the inverse of each of the following functions.
f: x
6x + 5, x = R
x + 4
bf:x→
C
e
f
f:
HX:
f: x42x, x € R
2x + 7
3
2x³ +5, x = R
1
f:
: x →
с
f: xH
g f: x
+ IM
H
X
f: x →
XER
9
5
4
5
X
2
XER
X - 1
h_f:x → (x+2)² + 7, x € Rand x
csusa-fl.schoology.com
+4, x € Rand x 0
i
f : x → (2x − 3)² – 5, x ≤ Rand x >
x = Rand x 1
2
j f:x x² - 6x, x € Rand x > 3
2 A function is called self-inverse if f (x) = f¯¹ (x) for all x in the domain. Show that the
following functions are self-inverse.
a
f : x → 5 – x,x ≤ R
b f:x-x,x = R
‚ x ≤ R and x ‡ 0
9
-2
32
ab] = ↓
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Transcribed Image Text:1:45 PM Fri Nov 25
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174%
a
1 Find the inverse of each of the following functions.
f: x
6x + 5, x = R
x + 4
bf:x→
C
e
f
f:
HX:
f: x42x, x € R
2x + 7
3
2x³ +5, x = R
1
f:
: x →
с
f: xH
g f: x
+ IM
H
X
f: x →
XER
9
5
4
5
X
2
XER
X - 1
h_f:x → (x+2)² + 7, x € Rand x
csusa-fl.schoology.com
+4, x € Rand x 0
i
f : x → (2x − 3)² – 5, x ≤ Rand x >
x = Rand x 1
2
j f:x x² - 6x, x € Rand x > 3
2 A function is called self-inverse if f (x) = f¯¹ (x) for all x in the domain. Show that the
following functions are self-inverse.
a
f : x → 5 – x,x ≤ R
b f:x-x,x = R
‚ x ≤ R and x ‡ 0
9
-2
32
ab] = ↓
50%
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