Q1 (a) The function f and g are defined as follows: f:x → |x], where x € [-4, 4], g:x → x|x|, where x E [-4,4]. i) Find the range of f and the range of g. ii) Show that f is not a one to one function and g is a one to one function, iii) Find the inverse function of g. (b) The function h is defined as h: R → R† such that h(x) = x². Show that h is a onto function but h is not a one to one function. (c) The function l is defined as l: R+ → R such that l(x) = In(2x + V4x² + 1). Show that %3D l is a onto function and l is a one to one function. Find the inverse function of l.
Q1 (a) The function f and g are defined as follows: f:x → |x], where x € [-4, 4], g:x → x|x|, where x E [-4,4]. i) Find the range of f and the range of g. ii) Show that f is not a one to one function and g is a one to one function, iii) Find the inverse function of g. (b) The function h is defined as h: R → R† such that h(x) = x². Show that h is a onto function but h is not a one to one function. (c) The function l is defined as l: R+ → R such that l(x) = In(2x + V4x² + 1). Show that %3D l is a onto function and l is a one to one function. Find the inverse function of l.
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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![Q1 (a)
The function f and g are defined as follows:
f:x → |x], where x E [-4, 4],
g:x → x|x|, where x E [-4,4].
i)
Find the range of f and the range
of
g.
ii)
Show that f is not a one to one function and g is a one to one function,
iii)
Find the inverse function of g.
(b)
The function h is defined as h: R → R† such that h(x) = x². Show that h is a onto
function but h is not a one to one function.
(c)
The function l is defined as l: R+ → R such that l(x) = In(2x + V4x2 + 1). Show that
l is a onto function and l is a one to one function. Find the inverse function of l.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F70d86970-59e6-4750-a0d7-1a72be8e9bdd%2Fe075c53a-588c-403b-b670-85ad011d4f34%2F34gwgz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Q1 (a)
The function f and g are defined as follows:
f:x → |x], where x E [-4, 4],
g:x → x|x|, where x E [-4,4].
i)
Find the range of f and the range
of
g.
ii)
Show that f is not a one to one function and g is a one to one function,
iii)
Find the inverse function of g.
(b)
The function h is defined as h: R → R† such that h(x) = x². Show that h is a onto
function but h is not a one to one function.
(c)
The function l is defined as l: R+ → R such that l(x) = In(2x + V4x2 + 1). Show that
l is a onto function and l is a one to one function. Find the inverse function of l.
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