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

[Jaco Viljoen]

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)=8Thank you

Homework Equations

g(x)=-(1/2)x-3
4^(gx)=8

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,

 

[Ray Vickson]

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)=8Thank you

Homework Equations

g(x)=-(1/2)x-3
4^(gx)=8

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,

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.

 

[RUber]

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.

 

[Jaco Viljoen]

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.

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

 

[Jaco Viljoen]

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.

Ruber,
I realized 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.

 

[Ray Vickson]

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

Yes, you did it correctly.

 

[Mark44]

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

gx makes no sense in this context. The equation you want to solve is $$4^{g(x)} = 8$$

Thank you

Homework Equations

g(x)=-(1/2)x-3
4^(gx)=8

See above.

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,

 

[Jaco Viljoen]

gx makes no sense in this context. The equation you want to solve is
$$4^{g(x)}=8$$

Hi Mark,
You are correct, I omitted the parentheses accidentally.
Thank you

 

[SammyS]

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.

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.

 

[Mark44]

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.

Actually, those two expressions are equivalent.

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

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]