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(4) For the functions f(x) = Vx - 3 and g(x) = vx + 2, find and determine the domain in each case: (a) gf %3D (b) f+g (5) For the functions f(x) and g(x) 3 + 4, find f(g(x)) and g(f(x)), hence or х— 4 X otherwise determine whether g(x) is the inverse of f(x).

(4) For the functions f(x) = Vx - 3 and g(x) = vx + 2, find and determine the domain in each case: (a) gf %3D (b) f+g (5) For the functions f(x) and g(x) 3 + 4, find f(g(x)) and g(f(x)), hence or х— 4 X otherwise determine whether g(x) is the inverse of f(x).

Advanced Engineering Mathematics
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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Need help with question 4 and 5

(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 and g(x) 3 (5) For the functions f(x) ==+ 4, find f(g(x)) and g(f(x)), hence or х— 4 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 x2 – 22 x – 24. (b) Hence, by use of long divison, find all remaining factors of the expression.
Transcribed Image Text:(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 and g(x) 3 (5) For the functions f(x) ==+ 4, find f(g(x)) and g(f(x)), hence or х— 4 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 x2 – 22 x – 24. (b) Hence, by use of long divison, find all remaining factors of the expression.
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