Question 3. Define a function f: R→ R as follows:For all real number x, f(x) = 16x-5.Then f is both one-to-one and onto. Find the inverse function f¹[5 points]

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Answered: Question 3. Define a function f: R → R…

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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2. For the given functions, i) f(x)=2+ x ii) f(x)= Vx+1, x2-1 3x iii) f(x)=- x +2 Find the following information: a) Graph of the function. b) Show that the function is one to one by using the Horizontal Line Test. c) Find the inverse function. d) Graph the inverse function on the same set axis. Remark on the symmetry of both graphs. e) How are the domains and the range of both the function and it's inverse related to each other?
Consider the following functions mapping Real numbers to Real numbers. a. f(x) = 2x b. f(x) = x³ c. f(x) = (x+4)/3 Determine for each of the above three functions. d. If the function has inverse, and e. In case it has inverse provide its inverse f-¹.
Consider the function: g(x) = with the domain R\(9} (i.e. all real numbers except 9) and the image R\{1} (i.e. all real numbers except 1). Find the expression for the inverse function g(x). Select one: O (5+9x)/(x+1) O 5+9x (x-9)/(x+5) O not in the list (5+9x)/(x-1)
Consider the function: g(z) = with the domain IR\{8} (i.e. all real numbers except 8) and the image R\{1} (i.e. all real numbers I+10 except 1). Find the expression for the inverse function g(r). Select one: O not in the list O (10+8x)/(x-1) O 10+8x O (10+8x)/(x+1) O (x-8)/(x+10)
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.
Determine the equation of the înverse function below! state whethen the imverse function on a relation. is

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Question 3. Define a function f: R → R as follows: For all real number x, f(x) = 16x-5. Then f is both one-to-one and onto. Find the inverse function f¹ [5 points]