# Thread: Making 'x' the subject of this formula - different

1. ## Making 'x' the subject of this formula - different

hello all,

i am thinking that i am lacking a few fundamental algebraic techniques to solve this, but i'm looking towards your help, thank you

Problem Statement: Make 'x' the subject of the formula:

Q1:
$e^x+x=4+y$

Q2:
$2+x^2+tan(3x/2)=y$

- str33tl0rd

2. Originally Posted by str33tl0rd
hello all,

i am thinking that i am lacking a few fundamental algebraic techniques to solve this, but i'm looking towards your help, thank you

Problem Statement: Make 'x' the subject of the formula:

Q1:
$e^x+x=4+y$

Q2:
$2+x^2+tan(3x/2)=y$

- str33tl0rd
Put simply, $x$ can't be made the subject in either of those equations.

3. Originally Posted by str33tl0rd
hello all,

i am thinking that i am lacking a few fundamental algebraic techniques to solve this, but i'm looking towards your help, thank you

Problem Statement: Make 'x' the subject of the formula:

Q1:
$e^x+x=4+y$

Q2:
$2+x^2+tan(3x/2)=y$

- str33tl0rd
Not possible. (Actually, the first can be done using the Lambert W-function which I'm sure you know nothing about). Why do you want to do this? Where have the questions come from?

4. wow, i never knew this would be some advanced university thing....thats why it gave me an headache for 5 hours to try figure it out and still not getting an answer....i was working on inverses of exponentials, trigonometric and logarithimic functions when i hit this question...i was to find the inverse of something similar. I took on firstly interchanging the x and y values....but then when i tried to make the 'y' value the subject of the formula, i just couldn't...

i found this type of question on the Stewart's Calculus 6th Edition....btw, i'm only in year 10 (16 years of age), so i won't know a great deal of things about Lambert and so..but i hope i will get a knowledge of them in these upcoming holidays....

but thanks for you help.

5. Originally Posted by str33tl0rd
wow, i never knew this would be some advanced university thing....thats why it gave me an headache for 5 hours to try figure it out and still not getting an answer....i was working on inverses of exponentials, trigonometric and logarithimic functions when i hit this question...i was to find the inverse of something similar. I took on firstly interchanging the x and y values....but then when i tried to make the 'y' value the subject of the formula, i just couldn't...

i found this type of question on the Stewart's Calculus 6th Edition....btw, i'm only in year 10 (16 years of age), so i won't know a great deal of things about Lambert and so..but i hope i will get a knowledge of them in these upcoming holidays....

but thanks for you help.
You could post the original question (or an example of someyjomh similar) from Stewart.

CB

6. i don't really have a problem with the actual inverse question, what caught my attention and took my time was making x the subject of such expressions; but if you still are really interested in doing that inverse question, here it is :

if $f(x)=3+x+e^x$
$calculate f^-(4)$

- str33tl0rd

7. Originally Posted by str33tl0rd
i don't really have a problem with the actual inverse question, what caught my attention and took my time was making x the subject of such expressions; but if you still are really interested in doing that inverse question, here it is :

if $f(x)=3+x+e^x$
$calculate f^-(4)$

- str33tl0rd
If you had posted the actual question right from the start less time would have been wasted. Because you do not need to find the general inverse function and then substitute x = 4.

Instead, note that $y = f^{-1}(4)$ where $4 = 3 + y + e^y \Rightarrow e^y + y = 1$. By inspection (and the question has been cooked for this to happen), y = 0. Therefore $f^{-1}(4) = 0$.

8. yep, nice working out mate; we got the same answers...
no time was wasted, as the descriptive title says here: making 'x' the subject of the formula, not solving the inverse function

thanks again

- str33tl0rd

9. Originally Posted by str33tl0rd
yep, nice working out mate; we got the same answers...
no time was wasted, as the descriptive title says here: making 'x' the subject of the formula, not solving the inverse function

thanks again

- str33tl0rd
The time you wasted was evidentialy not yours but ours.

CB

10. mate, i just asked a question....and i got my answer and i thanked you guys numerous times....then one of you guys started the thing again by asking what was the actual question...that wasn't my problem..so whoever asked, basically wasted his/her time and yours too

-str33tl0rd

11. Originally Posted by str33tl0rd
mate, i just asked a question....and i got my answer and i thanked you guys numerous times....then one of you guys started the thing again by asking what was the actual question...that wasn't my problem..so whoever asked, basically wasted his/her time and yours too