Functions of the n-th power (1 Viewer)

[sasquatch]

Regarding functions of the n-th power, i think i understand how to graph them when for example the question asks "Sketch y = f(x)³ when f(x) = x(x² - 3)". But im confused as to what i to do if for example the question does not specify a equation, only a drawing and asks to graph say [f(x)]⁴.

Also another question. Terry Lee (5th Edition) refers to f²(x) as being [f(x)]². On a page at wikipedia, it stated that f²(x) actually means the "function of the function of x" or better yet f[f(x)]. If a question in the HSC asks to graph f²(x), what do I take it as?

 

[SeDaTeD]

They won't write it like that in the HSC. If it did though, I think it'd be too damn hard to do f(f(x)) so make of that what you will.

 

[sasquatch]

Um ok thanks.

 

[sasquatch]

I would also like to ask stuff about sketching the primitive function, given a graph f(x).

These are some steps i figured out...

- Min/Max. t.p.s become points of inflexion
- x-intercepts become turning points
- If in a domain:
---- f(x) is negative, primitive of f(x) will be decreasing
---- f(x) is positive, primitive of f(x) will be increasing

What else is there... and how accurate do these graphs have to be. Oh yeah and what happens to points of inflexion from f(x) to the primitive of f(x).

 

[acullen]

Also another question. Terry Lee (5th Edition) refers to f²(x) as being [f(x)]². On a page at wikipedia, it stated that f²(x) actually means the "function of the function of x" or better yet f[f(x)]. If a question in the HSC asks to graph f²(x), what do I take it as?

When we did Taylor series at uni, we used the f⁽ⁿ⁾(x) notation to indicate "The nth derivative of function x". This was because the 6th derivative tends to look confusing when you notate it as f''''''(x). I'm pretty sure in the HSC they would write f[f(x)] if they ask a question on this.

Edit: Crap, I forgot the parentheses. Fixed now.

 

[buchanan]

f⁽ⁿ⁾(x) is the n-th derivative of f(x)

fⁿ(x) is the n-th iteration of f(x)

(f(x))<SUP>n</SUP> is the n-th power of f(x).

 

[sasquatch]

f⁽ⁿ⁾(x) is the n-th derivative of f(x)

fⁿ(x) is the n-th iteration of f(x)

(f(x))<SUP>n</SUP> is the n-th power of f(x).

So... terry lees a dickhead then..yeah?