(1) For the function f(x) evaluate and simplify the following: x² + 3' (c) f(x² + 3) (d) f-1) a (a) f(-1) (b) f(2a)

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Chapter2: Second-order Linear Odes
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Problem Set: A
х+1
(1) For the function f(x)
,evaluate and simplify the following:
x2 + 3'
a
(a) f(-1)
(b) f(2a)
(c) f(x? + 3) (d) fG-1
(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(()
(b) fg
(c)
(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) =,
X- 4
and g(x) = + 4, find f(g(x)) and g(f(x)), hence or
X
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 x? – 22 x – 24.
(b) Hence, by use of long divison, find all remaining factors of the expression.
Transcribed Image Text:Problem Set: A х+1 (1) For the function f(x) ,evaluate and simplify the following: x2 + 3' a (a) f(-1) (b) f(2a) (c) f(x? + 3) (d) fG-1 (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(() (b) fg (c) (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) =, X- 4 and g(x) = + 4, find f(g(x)) and g(f(x)), hence or X 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 x? – 22 x – 24. (b) Hence, by use of long divison, find all remaining factors of the expression.
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