The Student Room Group
Uni students - Complete our survey >>
Uni students - Complete our survey >>
Uni students - Complete our survey >>

functions maths help

g(2x +1) = ax + b
find g(x)
how to do this?
Original post by richmanswagoh
g(2x +1) = ax + b
find g(x)
how to do this?


For an easy to explain method, use the substitution u=2x+1 because that way the LHS becomes g(u), and now figure out what the RHS must be in terms of u.

Then replace u with x everywhere for the final answer.
im sorry but im confused
Original post by RDKGames
For an easy to explain method, use the substitution u=2x+1 because that way the LHS becomes g(u), and now figure out what the RHS must be in terms of u.

Then replace u with x everywhere for the final answer.
Original post by richmanswagoh
im sorry but im confused


With which part?
i dont get what you mean by 'u'


Original post by RDKGames
With which part?
Original post by richmanswagoh
i dont get what you mean by 'u'


It’s just a dummy variable you’re using to get

g(u) = (something)

before you get rid off it by replacing every u with x to get

g(x) = (something)



Thats the motivation behind it
so its basically like using y in inverse functions and then in the last step you swap with x.
but pls could you show me how you do it
Original post by RDKGames
It’s just a dummy variable you’re using to get

g(u) = (something)

before you get rid off it by replacing every u with x to get

g(x) = (something)



Thats the motivation behind it
Original post by richmanswagoh
so its basically like using y in inverse functions and then in the last step you swap with x.
but pls could you show me how you do it


Similar to that, yes.

I’ve described my approach in full, not sure what you want me to show..?
like your working out and the answer
Original post by RDKGames
Similar to that, yes.

I’ve described my approach in full, not sure what you want me to show..?
Original post by richmanswagoh
like your working out and the answer


No, you can do it.

If I did it for you, you’d be hitting your head on the table for missing the simplicity of it.


I already said, we use u=2x+1 so when it comes to the RHS of your function, you need to replace x by something in terms of u... so clearly you should rearrange the dummy substitution for x and use that as the replacement.
(edited 4 years ago)
so
u=2x+1
u-1=2x
u-1/2=x
therefore f(x)=a(x-1/2)=b??
Original post by RDKGames
No, you can do it.

If I did it for you, you’d be hitting your head on the table for missing the simplicity of it.


I already said, we use u=2x+1 so when it comes to the RHS of your function, you need to replace x by something in terms of u... so clearly you should rearrange the dummy substitution for x and put that into the function.
(edited 4 years ago)
Original post by richmanswagoh
so
u=2x+1
u-1=2x
u-1/2=x
therefore f(x)=x-1/2??


You now need to sub

x=(u-1)/2

into

ax + b


Simplify and the result is g(u).
so a(x-1/2) + b and then i expand
Original post by RDKGames
You now need to sub in

x=(u-1)/2

into

ax + b


Simplify and the result is g(u).

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you