onsider the following function. f(x) = x³ +9 (a) Find the inverse function of f. f-1(x) = (b) Graph both fand f-1 on the same set of coordinate axes. V

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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Consider the following function
onsider the following function.
f(x) = x³ +9
(a) Find the inverse function of f.
f-1(x) =
(b) Graph both fand f-1 on the same set of coordinate axes.
y
15
10
-15 -10 -5/
10
15
-5
10
-15
f
f f
y
y
15
15
10
10
5
-15 -10 -5
10
15
-15 -10 -5
10
15
-5
-5
-10-
10
-15
15
(c) Describe the relationship between the graphs of f and f-1.
O The graph of f-1 is the reflection of f in the line y = x.
O The graph of f-1 is the reflection of f in the y-axis.
O The graph of f-1 is the reflection of f in the line y = -x.
O The graph of f-1 is the same as the graph of f.
O The graph of f-1 is the reflection of f in the x-axis.
domain
(d) State the domain and range of f. (Enter your answers using interval notation.)
range
X
domain
-15 -10
State the domain and range of f-1. (Enter your answers using interval notation.)
range
-5
y
15
10
15
10 15
X
Transcribed Image Text:onsider the following function. f(x) = x³ +9 (a) Find the inverse function of f. f-1(x) = (b) Graph both fand f-1 on the same set of coordinate axes. y 15 10 -15 -10 -5/ 10 15 -5 10 -15 f f f y y 15 15 10 10 5 -15 -10 -5 10 15 -15 -10 -5 10 15 -5 -5 -10- 10 -15 15 (c) Describe the relationship between the graphs of f and f-1. O The graph of f-1 is the reflection of f in the line y = x. O The graph of f-1 is the reflection of f in the y-axis. O The graph of f-1 is the reflection of f in the line y = -x. O The graph of f-1 is the same as the graph of f. O The graph of f-1 is the reflection of f in the x-axis. domain (d) State the domain and range of f. (Enter your answers using interval notation.) range X domain -15 -10 State the domain and range of f-1. (Enter your answers using interval notation.) range -5 y 15 10 15 10 15 X
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