5. a) Define the following with an example: i) Domain of a function ii) One – to – one function 4x +1 b) A function f is defined on the det of real numbers by f(x) 2x – 3 i) Write down the domain of f. ii) Show that fis a one – to – one function. - iii) Find the inverse of the function f. c) Given the function f(x) = x², g(x)= 3x – 4, find the composite function - gofl (where g • fl -1 means f-'followed by g}

5. a) Define the following with an example: i) Domain of a function ii) One – to – one function 4x +1 b) A function f is defined on the det of real numbers by f(x) 2x – 3 i) Write down the domain of f. ii) Show that fis a one – to – one function. - iii) Find the inverse of the function f. c) Given the function f(x) = x², g(x)= 3x – 4, find the composite function - gofl (where g • fl -1 means f-'followed by g}

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

5. a) Define the following with an example:
i) Domain of a function
ii) One – to – one function
4x +1
A function fis defined on the det of real numbers by f(x) =
b)
2x - 3
i) Write down the domain of f.
ii) Show that fis a one - to – one function.
iii) Find the inverse of the function f.
c) Given the function f(x) = x², g(x)= 3x – 4, find the
composite function
-
gofl (where gof"l
means f-followed by g}
d) A function f is defined on the set N of natural
numbers by
A0) = 2, A2) = 5 and f(n) = 2 fAn - 1) + 3 An - 2) + An - 3)
%3D
for all n 2 3. Find (4).

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