find the domain of f[tex]f(x) = \frac{x}{2x - 1} [/tex][tex]f(x) = \frac{2x - 7}{x ^{2} + 8x + 7} [/tex]

Answers:
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Question 1)  The domain of the function is:

" x =  {x | x ≠ [tex] \frac{1}{2} [/tex]} " . 
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Question 2)  The domain of the function is:

" x =  {x | x ≠ -7, -1 ]} " . " 
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Explanations:
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Explanation for "Question 1" ; 

The denominator cannot equal "0".

So; set the "denominator" equal to "0" ; as follows:

  →   2x - 1 = 0 ; 

Add "1" to each side of the equation:

2x - 1 + 1 = 0 + 1 ; 

2x = 1 ; 

Divide each side of the equation by "2" ; 

2x/2 = 1/2 ; 

to get:  "x = 1/2" .
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Answer:  The domain is:  " {x | x ≠ [tex] \frac{1}{2} [/tex]} " . 
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Explanation for:  "Question 2" )
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The denominator cannot equal "0";  
→ {since one cannot "divide by 0" } ; 

→ So; set the "denominator" equal to "0" ; 

→  (x² + 8x + 7) = 0 ;   Factor:
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(x + 7) (x + 1) = 0 ; 

x = -7 ; x = -1 ; 
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Answer:  
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The domain of the function is:
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       "  x =  {x | x ≠ -7, -1 ]} " . 
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