Solving for Inverse

[Panicmode]

I have a question, which method does everyone use to solve the inverse? I usually solve for the inverse using the following method;

f(f^-1(x))=x
then sole for f^-1(x)


I never learnt the other method. What is it?

Oh, also a tip for sketching the inverse I just found out recently;;

Fold the bottom right corner of your page up so that you have a small triangle.
On the folded up bit sketch the graph of the original function.
Fold the corner bk down and trace over the graph; this is your inverse =D.

When I learnt this I have to admit my mind was slightly blown.

[Greatness]

f(f^-1(x))=x
then sole for f^-1(x)

What method is this? Is it the same as:
f(x)= 2x+3
swap x and y
x=2y+3
so f^-1(x)=1/2(x-3)

[abeybaby]

the method that pretty much everyone uses is just:
sway x and y, then solve for y

[REBORN]

Is there even any other method to find an inverse except swapping x and y? :S

[luffy]

f(f^-1(x))=x
then sole for f^-1(x)

What method is this? Is it the same as:
f(x)= 2x+3
swap x and y
x=2y+3
so f^-1(x)=1/2(x-3)

Yes the two methods are, in fact, exactly the same. Think about it.

When you write "inverse, swap x and y", your pretty much doing f(y) = x. When you get the y-value, you can just change it to f^-1(x). "Panicmode" just stated f(f^-1(x)) = x i.e. f(y) = x, which means the two methods are essentially the same.

[b^3]

I think the essentials book may have gone through booth methods, but swapping x and y is the only one that is worth remembering, the other one is pointless.

Although when solving for when the inverse and the original intersect, f(x)=x is easier than f(x)=f^-1(x)

EDIT: now seen luffy's post.

[paulsterio]

When you do an inverse you have to write "For inverse, swap and " otherwise you lose a mark yeah?

[nacho]

When you do an inverse you have to write "For inverse, swap and " otherwise you lose a mark yeah?

yep, or it's algebraically retarded !

[Greatness]

When you write the inverse equation, do you have to write out the equation with the domain so it's like:
f: R -> R  where f^-1(x)=.....
or can you just write f^-1(x)=.... for [a,b] ? Does it matter?

[luken93]

I usually just do top line;

"Let f(x) = y, Inverse swap x and y"
...Proceed with rearranging...
y = .....
"Since it is an inverse function, f^-1(x) = ...., x c [a, b]"

[abeybaby]

If you dont write swap x and y for inverse, its not as if you WILL lose a mark, but they CAN take the mark, cos the line is not true.

and @swarley, theres no difference. also, it should be f^-1: domain -> R  where f^-1(x)=....., not f: R -> R  where f^-1(x)=.....

[Greatness]

If you dont write swap x and y for inverse, its not as if you WILL lose a mark, but they CAN take the mark, cos the line is not true.

and @swarley, theres no difference. also, it should be f^-1: domain -> R  where f^-1(x)=....., not f: R -> R  where f^-1(x)=.....

Sweet thanks! another careless error...

[Panicmode]

f(f^-1(x))=x
then sole for f^-1(x)

What method is this? Is it the same as:
f(x)= 2x+3
swap x and y
x=2y+3
so f^-1(x)=1/2(x-3)

Yes the two methods are, in fact, exactly the same. Think about it.

When you write "inverse, swap x and y", your pretty much doing f(y) = x. When you get the y-value, you can just change it to f^-1(x). "Panicmode" just stated f(f^-1(x)) = x i.e. f(y) = x, which means the two methods are essentially the same.

Lol, just noticed this I think my teacher didn't teach us "swap x and y" because he wanted to avoid loosing marks for correct notation. lol.

[VivaTequila]

I normally just say let x=f(y) and then expand the f(y) to whatever the function is and solve, is that wrong?

[abeybaby]

I normally just say let x=f(y) and then expand the f(y) to whatever the function is and solve, is that wrong?

nah thats completely fine...