Theorem 5 Theorem If f and g are continuous at a and e is a constant, then the following functions are (a) Any polynomial is continuous also continuous at a: everywhere; that is, it is continuous 1f+9 on 2. -9 TR =(00, 00) 3. ef (a) Any rational function is continuous 4. fg wherever it is defined; that is, it is f if g(a) 0 5. continuous on its domain The following types of functions are continuous at every number in their domains: polynomials rational functions 9 Theorem root functions trigonometric functions inverse trigonometric functions If g is continuous at a and f is continuous at g(a), then the composite function fo g given by (fo g)() = f(g(#)) is exponential functions logarithmic functions continuous at a. Theorem 7 25, 26, 27, 28, 29, 3o, 31 and 32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 25. F(22-2-1 21

Question

Please answer this questions using the theorems 

Theorem
5 Theorem
If f and g are continuous at a and e is a
constant, then the following functions are
(a) Any polynomial is continuous
also continuous at a:
everywhere; that is, it is continuous
1f+9
on
2. -9
TR =(00, 00)
3. ef
(a) Any rational function is continuous
4. fg
wherever it is defined; that is, it is
f
if g(a) 0
5.
continuous on its domain
The following types of functions are
continuous at every number in their
domains:
polynomials
rational functions
9 Theorem
root functions
trigonometric functions
inverse trigonometric functions
If g is continuous at a and f is continuous
at g(a), then the composite function fo g
given by (fo g)() = f(g(#)) is
exponential functions
logarithmic functions
continuous at a.
Theorem 7
25, 26, 27, 28, 29, 3o, 31 and 32 Explain, using Theorems 4, 5, 7, and 9, why the function is
continuous at every number in its domain. State the domain.
25. F(22-2-1
21

Image Transcription

Theorem 5 Theorem If f and g are continuous at a and e is a constant, then the following functions are (a) Any polynomial is continuous also continuous at a: everywhere; that is, it is continuous 1f+9 on 2. -9 TR =(00, 00) 3. ef (a) Any rational function is continuous 4. fg wherever it is defined; that is, it is f if g(a) 0 5. continuous on its domain The following types of functions are continuous at every number in their domains: polynomials rational functions 9 Theorem root functions trigonometric functions inverse trigonometric functions If g is continuous at a and f is continuous at g(a), then the composite function fo g given by (fo g)() = f(g(#)) is exponential functions logarithmic functions continuous at a. Theorem 7 25, 26, 27, 28, 29, 3o, 31 and 32 Explain, using Theorems 4, 5, 7, and 9, why the function is continuous at every number in its domain. State the domain. 25. F(22-2-1 21

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