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anonymous

  • one year ago

Given the following functions f(x) and g(x), solve f[g(6)] and select the correct answer below: f(x) = 6x + 12 g(x) = x − 8

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  1. mathstudent55
    • one year ago
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    First, find g(6). Then use that value in function f.

  2. mathstudent55
    • one year ago
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    What is function g evaluated at x = 6? g(x) = x - 8 g(6) = 6 - 8 g(6) = ?

  3. anonymous
    • one year ago
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    -2 ?

  4. anonymous
    • one year ago
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    So , the answer would be 0 because 6(-2)+12=0 Right ?

  5. mathstudent55
    • one year ago
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    Correct.

  6. anonymous
    • one year ago
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    Thank you so much ! Can I ask another one ?

  7. mathstudent55
    • one year ago
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    f(g(x)) = f(x - 8) = 6(x - 8) + 12 f(g(2)) = 6(2 - 8) + 12 = 6(-6) + 12 = -12 + 12 = 0

  8. mathstudent55
    • one year ago
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    You're welcome. Yes, go ahead.

  9. anonymous
    • one year ago
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    Given the following functions f(x) and g(x), solve f over g(−4) and select the correct answer below: f(x) = 4x − 4 g(x) = x − 1

  10. mathstudent55
    • one year ago
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    \(\dfrac{f}{g}(x) = \dfrac{f(x)}{g(x)} = \dfrac{4x - 4}{x - 1} = \dfrac{4(x - 1)}{x - 1} = 4\) Since \(\dfrac{f}{g}(x) = 4\), no matter what x is, \(\dfrac{f}{g}(-4) = 4\)

  11. anonymous
    • one year ago
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    So technically x=4 ?

  12. mathstudent55
    • one year ago
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    No. In this problem, you were asked to find the value of the quotient of the functions at x = -4. For any value of x, the value of the quotient of the functions is 4, with only one exception, which is at x = 1. This division of functions is undefined at x = 1 because it involves division by zero. For all other values of x, the division of these two functions is 4.

  13. UsukiDoll
    • one year ago
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    @mathstudent55 factored a 4 out and was able to cancel x-1 so we don't have to evaluate when x = -4 anymore we just have 4

  14. UsukiDoll
    • one year ago
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    |dw:1437445518445:dw|

  15. anonymous
    • one year ago
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    So after you distribute for f(x) and figure out g(x) the answer will be 4

  16. anonymous
    • one year ago
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    & of course after you divide both solutions.

  17. UsukiDoll
    • one year ago
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    the question asked to find f/g (-4) which means finding f(x) ---- g(x) first which is 4x-4 ---------- x-1 since we can factor a 4 out of the numerator the x-1 is present in the numerator and the denominator so that's canceled out. So, we're just left with a 4. Since there is no variable attached to the 4, that's the answer if we had 4x. Then we have to evaluate when x = -4.

  18. UsukiDoll
    • one year ago
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    yes the answer is just 4

  19. anonymous
    • one year ago
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    Thaaankkk yooouuu !

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