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Suppose function g is defined as follows: g(x)=-(1/2)x-3

  1. Jun 29, 2015 #1
    Suppose the function g is defined as follows:
    g(x)=-(1/2)x-3
    Write down the D:g and solve the equation 4^(gx)=8


    Thank you


    2. Relevant equations
    g(x)=-(1/2)x-3
    4^(gx)=8
    3. The attempt at a solution
    D:g (-∞,∞) because the function is a line,
    4^((-1/2)x-3)=8
    log4^((-1/2)x-3)=log8
    (-1/2x)-3=(log8)/(log4)
    (-1/2x)-3=1.5
    (-1/2x)=4.5 add 3 to both sides
    x=-9

    Have I got it right?
    Thank you,
     
  2. jcsd
  3. Jun 29, 2015 #2

    Ray Vickson

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    You can check this for yourself: plug in x = -9 and see if it works! You should develop, as a matter if routine, the habit of checking your own work. There will be many times (for example, on exams) when the option of asking questions on-line is unavailable to you, and you should try not to rely on it.
     
  4. Jun 29, 2015 #3

    RUber

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    That is correct, but you got sloppy with your parentheses.
    You started with (-1/2)x - 3 and then switched at some point to (-1/2x)-3. These are different expressions meaning ## -\frac12 x - 3 ## or ## -\frac{1}{2 x} - 3 ##.
    Luckily, you knew that you meant and solved for x correctly.
     
  5. Jun 29, 2015 #4
    Hi Ray,
    Thank you for the reply,
    -9 is correct, I have checked it.
    I just want a confirmation that I did the right thing with regards to the question.
    Thank you again,

    Jaco
     
  6. Jun 29, 2015 #5
    Ruber,
    I realised that my parentheses were wrong and changed them after from-1/(2x) which was also wrong, must have missed a coupleor corrected them incorrectly,
    I write my work out first and then retype in the forum.

    I do need some practice with the typing as I often make this error,
    Thank you.
     
  7. Jun 29, 2015 #6

    Ray Vickson

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    Yes, you did it correctly.
     
  8. Jun 29, 2015 #7

    Mark44

    Staff: Mentor

    gx makes no sense in this context. The equation you want to solve is $$4^{g(x)} = 8$$
    See above.
     
  9. Jun 29, 2015 #8
    Hi Mark,
    You are correct, I omitted the parentheses accidentally.
    Thank you
     
  10. Jun 29, 2015 #9

    SammyS

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    Actually, those two expressions are equivalent.

    -1/2x ##\displaystyle\ =-\frac{1}{2}x\ .##

    Added in Edit:
    As Mark points out below, writing the expression in this manner is bad practice.
     
    Last edited: Jun 29, 2015
  11. Jun 29, 2015 #10

    Mark44

    Staff: Mentor

    And a constant source of confusion for the ones reading things like "-1/2x". The proper interpretation is as Sammy wrote: -1/2 times x, but we are torn between wondering whether the person who wrote this understands the rules of precedence, or not.[/quote]
     
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