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.
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.
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
ChapterP: Prerequisites
SectionP.5: Functions
Problem 9ECP
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe6ea114-e96e-411f-a3e3-9bd506176baa%2F898c7ffe-d78b-4cc0-88bc-8e45954c93ea%2Fjmbx0ti_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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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Follow-up Question
i dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?
Solution
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