Transformations (1 Viewer)

[Sunyata]

Hi

Could someone please explain to me how to do transformations for:

f(x^2)
inverse sin (x)
inverse cos (x)
inverse tan(x)

or suggest any resources i could use?

I had some in my exams and I totally failed them

Thanx

 

[Aquawhite]

Dunno if I know the transformations for the trig and I'm not quite sure how you mean it.

f(x^2) when transforming f(x) will simple mirror each other from right to left about the x-axis. What ever is on the right hand side of the graph will now be mirrored to the left... since all negative values will be positive.

Test it using winplot or something.

 

[Rezen]

do you mean how do you graph arcsin(x^2) arccos(x^2), etc.

It's the same process for any other function, its mirrored around the y axis, and its similar to f(x) except its sort of squished around x=1,-1, with the f(x) and f(x^2) intersecting at x=0, +-1.

go to wolframalpha.com and just type it in to see the graph of it if you need to.

edit: sorry, they dont necesarrily intersect at x=-1, it may be the reflection of f(x) around the x axis that will intersect at x=-1

 

[Sunyata]

Oops I meant

* f(x^2)
* arcsin f(x)
* arccos f(x)
* arctan f(x)

 

[Trebla]

Oops I meant

* f(x^2)
* arcsin f(x)
* arccos f(x)
* arctan f(x)

For the last three, list all the features of the simple y = arcsin/arccos/arctan x, then replace x with f(x) in those listed features and interpret those features to deduce your graph.
For the first one it is similar idea, but the other way around. List all the features of y = f(x) provided in the question and then replace x with x² and interpret those features to deduce your graph.

 

[Lukybear]

Let u = x^2
Draw f(u), then x^2
Take read u value of x^2 graph and place upon f(u)