3 and g(x) =+ 4, find f(g(x)) and g(f(x)), hence or 3 (5) For the functions f(x) : х — 4 otherwise determine whether g(x) is the inverse of f(x).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Question 5 please solve thoroughly 

in each case: (a) gf
(b) f+g
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:in each case: (a) gf (b) f+g 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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