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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.

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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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.
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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i dont understand the fourth and fifth row of equation of gh(x) and why the function is invalid?

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