Question

Find a formula for the inverse of each of the following functions.

Answer 1

\[W (x)=\left(\begin{matrix}1 \\ x\end{matrix}\right)\]

Answer 2

that is supossed to be a fraction...

Answer 3

What you need to do is to rearrange it so that the x is on the left on its own, and everything else is on the right... That way, you can put in whatever value y=w(x) and then you get a value x. That's kind of the idea involved in finding the inverse of a function. You go the other way...

Answer 4

Wait I am confused so you just inverse the equation by changing the sign...

Answer 5

No. You rearrange it. So, if you had y=3x+1, then it's easy to pick any x and then find a y. But if you wanted to pick any y and then find what x would be, then it's better to find an inverse of that function. That means that you want to rearrange it so that you can put in any value for y, and that tells you easily what x will be. So, rearranging y=3x+1 can give you x=(y-1)/3. See that on the right hand side you can plug in any value of y and then you quickly find what x must be... Now you can rewrite that as y^(-1)=(x-1)/3... just changing the name of x and y, where y^(-1) means something like "inverse of y" that's just aesthetics.

Answer 6

Do the same for your function above.

Answer 7

Can you help me do it? I am no good at this :/

Answer 8

y=w(x)=1/x .... rearrange so that x="some stuff with y in it..."

Answer 9

Also remember that y is the same as w(x)... depending on what you want to call it...

Answer 10

Wait so why is W(x)?

Answer 11

I am so confused sorry i am no good at this.

Answer 12

if you mean to find inverse of the function W=1/x

then you can rewrite it as y=1/x

now change the places of x and y with each other

x=1/y

now make y again the subject

x.y=1

y=1/x

1/x is the inverse!

Answer 13

Oh thanks hashsam!