  # Theorem5 TheoremIf f and g are continuous at a and e is aconstant, then the following functions are(a) Any polynomial is continuousalso continuous at a:everywhere; that is, it is continuous1f+9on2. -9TR =(00, 00)3. ef(a) Any rational function is continuous4. fgwherever it is defined; that is, it isfif g(a) 05.continuous on its domainThe following types of functions arecontinuous at every number in theirdomains:polynomialsrational functions9 Theoremroot functionstrigonometric functionsinverse trigonometric functionsIf g is continuous at a and f is continuousat g(a), then the composite function fo ggiven by (fo g)() = f(g(#)) isexponential functionslogarithmic functionscontinuous at a.Theorem 725, 26, 27, 28, 29, 3o, 31 and 32 Explain, using Theorems 4, 5, 7, and 9, why the function iscontinuous at every number in its domain. State the domain.25. F(22-2-121

Question help_outlineImage TranscriptioncloseTheorem 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 fullscreen
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Step 1

Consider the given rational function as  F(x)=2x2 – x –1/ (x2 +1).

Let the numerator and denominator of the above function be denoted as f(x)= 2x2 – x –1 and g(x)= x2 +1 respectively.

Since the numerator and ...

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