3,4,5 f:xx-4.XER8:x→1-√x-2.XES= (x:xER, x>k).Find the least value of k for which fog is a function.2. A function f is defined by f:xwhere-1 < x < 1. Test if f is odd or even and show thatfis strictly monotone increasing. Sketch the graph of f.3. The functions f, g and h aredefined byf:x→x³,XER8:x→ √√e* - 1,x40h: x→ In(x + 1),x>-1Determine if gh and hg can be formed.4. Functions f and g are defined byf: x→ loga x,x eR+, a> 1g:x → ½XER+State the range of f and g and show that if k denotes thecomposite function fg, then k(x) + f(x) = 0.5. The functions f, g and h are defined as follows:f: x → sin x,x > 08:x→> In (x²),XERh:x→x2-4XER(i) Explain briefly why the inverse function f andthe composite function fg cannot be formed.(ii) Give the largest possible domain of g so that thecomposite function fg can be formed. Write downits rule and state its range.

We shall solve first question only

Answered: 3. The functions f, g and h are defined…

3. The functions f, g and h are defined by f:x→x XER 8:x→ √e* - , x=0 h: x→ In(x + 1), x>-1 Determine if gh and hg can be formed.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.1: Polynomials Over A Ring

Problem 24E

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Question

3,4,5

f:xx-4.
XER
8:x→1-√x-2.
XES= (x:xER, x>k).
Find the least value of k for which fog is a function.
2. A function f is defined by f:x
where
-1 < x < 1. Test if f is odd or even and show that
fis strictly monotone increasing. Sketch the graph of f.
3. The functions f, g and h are
defined by
f:x→x³,
XER
8:x→ √√e* - 1,
x40
h: x→ In(x + 1),
x>-1
Determine if gh and hg can be formed.
4. Functions f and g are defined by
f: x→ loga x,
x eR+, a> 1
g:x → ½
XER+
State the range of f and g and show that if k denotes the
composite function fg, then k(x) + f(x) = 0.
5. The functions f, g and h are defined as follows:
f: x → sin x,
x > 0
8:x→
> In (x²),
XER
h:x→x2-4
XER
(i) Explain briefly why the inverse function f and
the composite function fg cannot be formed.
(ii) Give the largest possible domain of g so that the
composite function fg can be formed. Write down
its rule and state its range.

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