anonymous
  • anonymous
Given f(x) = x + 2 and g(x) = x2 – 4, find the function (g/f)(x). A. (g/f)(x) = x – 4, excluded value: x = -4. B. (g/f)(x) = x – 2, excluded value: x = -2. C. (g/f)(x) = x – 4, excluded value: x = 4. D. (g/f)(x) = x – 2, excluded value: x = 2
Algebra
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SOLVED
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katieb
  • katieb
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johnweldon1993
  • johnweldon1993
\[\frac{ x^2 - 4 }{ x + 2 }\] How many times does x go into x squared...? and how many times does 2 go into -4...?
jim_thompson5910
  • jim_thompson5910
alternatively, you can factor the numerator using the difference of squares rule
johnweldon1993
  • johnweldon1993
Yes or as @jim_thompson5910 suggests difference of square x² + 4 = (x + 2)(x - 2) Now you would have \[\frac{ (x + 2)(x - 2) }{ x + 2 }\] Notice how the (x + 2) would cancel out...and you would be left with...?

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anonymous
  • anonymous
x-2?
johnweldon1993
  • johnweldon1993
Perfect!
johnweldon1993
  • johnweldon1993
Now the excluded value part.....this is asking...what number...will make your denominator = 0? So x + 2 = 0 what does x equal?
johnweldon1993
  • johnweldon1993
*this is called an excluded value...because if the denominator of a fraction...= 0 ...the function is "undefined"
anonymous
  • anonymous
So x =0? lol it wont let me msg you back. So thank you! I'm terrible with math
johnweldon1993
  • johnweldon1993
not quite Your denominator.....is x + 2 to find an excluded value...we need to set this to 0...and solve for x x + 2 = 0 to solve for x....we need to isolate it...and subtract 2 from both sides... x + 2 = 0 -2 -2 x = -2
anonymous
  • anonymous
Okay got it. thank you!
johnweldon1993
  • johnweldon1993
no problem :)

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