Find the domain of f f(x) = (x)/(2x - 1) f(x) = (2x - 7)/(x ^(2) + 8x + 7)

Question

Find the domain of f


`f(x) = (x)/(2x - 1)`

`f(x) = (2x - 7)/(x ^(2) + 8x + 7)`

Answer 1

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

" x = {x | x ≠
`(1)/(2)`} " .
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Question 2) The domain of the function is:

" 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 ≠
`(1)/(2)`} " .
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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 " .
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