(2) State and use the appropriate formulae, find the sum of the odd numbers from 1 to 199, inclusive.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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QUESTION 2 &3

Problem Set: A
x+ 1
,evaluate and simplify the following:
(1) For the function f(x)
=-
x² + 3'
(c) f(x² +3) (d) f G- 1)
a
(a) f(–1)
(b) f(2a)
(2) State and use the appropriate formulae, find the sum of the odd numbers from 1 to 199,
inclusive.
(3) For the functions f(x) = 3x – 4 and g(x) = x + 2, find the following and determine
the domain in each case: (a) g((f)
f
(c)
g
(b) fg
(4) For the functions f(x) = Vx – 3 and g(x) = vx+ 2, find and determine the domain
in each case: (a) gf
(b) f+g
3
3
(5) For the functions f(x)
and g(x) = + 4, find f(g(x)) and g(f(x)), hence or
X- 4
otherwise determine whether g(x) is the inverse of f(x).
(6)
(a) Using the remainder theorem, determine whether (x – 4) and (x– 1) are factors
of the expression x³ + 3 x2 – 22 x – 24.
(b) Hence, by use of long divison, find all remaining factors of the expression.
Transcribed Image Text:Problem Set: A x+ 1 ,evaluate and simplify the following: (1) For the function f(x) =- x² + 3' (c) f(x² +3) (d) f G- 1) a (a) f(–1) (b) f(2a) (2) State and use the appropriate formulae, find the sum of the odd numbers from 1 to 199, inclusive. (3) For the functions f(x) = 3x – 4 and g(x) = x + 2, find the following and determine the domain in each case: (a) g((f) f (c) g (b) fg (4) For the functions f(x) = Vx – 3 and g(x) = vx+ 2, find and determine the domain in each case: (a) gf (b) f+g 3 3 (5) For the functions f(x) and g(x) = + 4, find f(g(x)) and g(f(x)), hence or X- 4 otherwise determine whether g(x) is the inverse of f(x). (6) (a) Using the remainder theorem, determine whether (x – 4) and (x– 1) are factors of the expression x³ + 3 x2 – 22 x – 24. (b) Hence, by use of long divison, find all remaining factors of the expression.
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