How Do You Calculate the Derivative of an Inverse Function?

[frasifrasi]

Ok,

We are asked to find

(f-1(3))' for f(x) = 3 + x^2 + tan(x*pi/2)

I think we are supposed to use the formula (f-1(x))' = 1/f'(f-1(x))

But I am not sure how to get f-1(3).
If someone can show me how to get that, it would be extremely helpful for me to understand how this works.

Thank you.

 

[rocomath]

What book are you using? You ask a lot of questions ... either your book really sucks, your teacher sucks, or you're not studying enough.

 

[Saladsamurai]

I think what rocophysics is saying, is that if you showed a little more work, we'd be more apt to help.

I would certainly think that he was not discouraging you from asking a lot of questions. God knows I do.

Casey

 

[frasifrasi]

My book doesn't go over this for some reason, it goes straight into inverse trig functions. I cannot get any firther without getting through that first step:

SO, 3 + x^2 + tan(x*pi/2) = 3

x^2 + tan(x*pi/2) = 0

I don't know how to find out when this happens...
If anyone can show me how, i would be able to gain some insight into this. If I had money I would pay someone to show me, but I am broke ok?

 

[Saladsamurai]

What happens when x=0?

Casey

 

[Feldoh]

f(x) = 3 + x^2 + tan(x*pi/2)

can you find f-1(x)? That would be a start

 

[frasifrasi]

No, I can't. Can you please show me how, that would be a tremendous help.

Also, what is the curve of r = sqrt(sin(X)) ?

I could not find it on my textbook.

 

[HallsofIvy]

If you are not going to pay any attention to the responses to your questions why ask?

As Casey said, what bloody happens when x= 0?

What do you mean by "what is the curve of r= sqrt(sin(X))? I know how to find the curve of a function in Cartesian coordinates and even in polar coordinates- but that is neither. You have to have some kind of coordinate system before you can talk about the "curve" corresponding to a function or equation!

 

[dbodow]

f(x) = 3 + x^2 + tan(x*pi/2)

can you find f-1(x)? That would be a start

hint: to find f-1(x), switch x and y everywhere in the equation and solve for y

 

[rocomath]

what is an inverse? refer back to a post where rock.freak had showed you.

https://www.physicsforums.com/showpost.php?p=1543556&postcount=5

what is the domain of:

\sqrt{x}

? how would you apply that to your 2nd problem?

 

[frasifrasi]

it is just it man ==> r^2 = sqrt(sin(X))
And what happens when x= 0?

<edit: MIH>

 

[rocomath]

it is just it man ==> r^2 = sqrt(sin(X))

<edit:MIH>

What exactly does it mean to say that x=0? How would you perform that operation mathematically?

 

[frasifrasi]

As I speak, tears are rolling down my cheeks. I have used x = 0 and arrived at the answer!


EDIT:

for the graph = x^2 + y^2 = sin x?
I don't really know what to do. We are just asked to find the curve bounded by r = (sin(x)^1/2 for 0 <= x <= pi/3

any hints?

 

[Feldoh]

f-1(x) of a function is usually done like this:

f(x) = y = x+1 for example

1.) Switch x's and y's, so we now have x = y+1
2.) Solve for y, so y = x-1 = f-1(x)

 

[rocomath]

As I speak, tears are rolling down my cheeks. I have used x = 0 and arrived at the answer!

You should check out some Precalculus books from the library.

It's always handy to have around.

 

[frasifrasi]

for the graph = x^2 + y^2 = sin x?
I don't really know what to do. We are just asked to find the curve bounded by r = (sin(x)^1/2 for 0 <= x <= pi/3

any hints?

 

[Saladsamurai]

for the graph = x^2 + y^2 = sin x?
I don't really know what to do. We are just asked to find the curve bounded by r = (sin(x)^1/2 for 0 <= x <= pi/3

any hints?

Does it say find the curve bounded by...? Or the area?

Casey