Maths Methods 3/4 Help Thread 2011

[xZero]

If we compute f(g(x)) before restricting the domain, then your saying that this function exist without any restriction to the domain, which may not be true

[luken93]

Ok, say for:

  and

For g(f(x)) to exist, I'd have to restrict the domain to or

But if I simply find g(f(x)) = , then the domain of this function is the same as above.

I think what I'm doing is sorta answering two different questions, 1 being find the domain of f(x) that would allow g(f(x)) to be definable, and then finding the domain of g(f(x))...


EDIT: I've worked it out.
This is probably a better example I was looking for:

and

- This would imply a domain of R\{0}

But the domain is the intersection of f(g(x)) and g(x) - which would be R\{0} intersecting with R\{2} = R\{0, 2}

[kefoo]

For f(x) = 2x^(3/5) + 6 find f^-1(x) and state the domain
For f(x) = 2x^(2/5) + 6 find the rule and domain for the inverse

the power stuffs me up, so if anyone knows how to do please help xD

[luken93]

x = 2y^(3/5) + 6
(x-6/2) = y^(3/5)
(x-6/2)^(5/3) = y^(3/5)(5/3)

y = (x/2)^(3/5)

[kefoo]

1. Given g(x) = asin(x)+bcos(x), g(pi/4) = 2*sqrt(2) and g(-pi/6) = -1, Find the values of a and b
2. Given that g(x) = |x| and f(x) = ln(2-x)
    i) State the maximal domain for each of the composite functions (fog and gof)
    ii) For fog(x), restrict its domain so that the function is 1-to-1 and hence find the rule for its inverse fuction which is f^-1(fog(x))

[Rairiko]

How would I work out this question?

For pi/2 < x < pi with cos x= -cos pi/6, find the value of x (do not evaluate cos pi/6)

[brightsky]

cos x = -cos pi/6
cos x = cos(pi - pi/6) = cos(5pi/6) [Only one within given domain]
so x = 5pi/6

[Rairiko]

cos x = -cos pi/6
cos x = cos(pi - pi/6) = cos(5pi/6) [Only one within given domain]
so x = 5pi/6

i was wondering how you made -cos pi/6 into cos (pi-pi/6)

[brightsky]

symmetry. cosine represents the x coordinates, and in the second quadrant, x is negative. the identity should be in the book: cos(pi - x) = - cos(x). there are a whole lot of similar identities that can be found using the unit circle and symmetry properties.

[taiga]

Stickied cuz it's a good as thread

[eeps]

Question...

It is known that f(0)=2 and f'(0)=4. Find d(loge(f(x)))/dx when x=0.

Any help would be greatly appreciated!

[Water]

Question...

It is known that f(0)=2 and f'(0)=4. Find d(loge(f(x)))/dx when x=0.

Any help would be greatly appreciated!

d (log e (fx) )/dx


Derivative would be

f'(x) x 1/ f(x)

= 4/2


= 2

[kedireturns]

How to define a function

[thushan]

A "mapping" between two sets of numbers. Eg:

x              f(x)
1              1
2              2
3              3
4              4

where x and f(x) may or may not be related. In this case, I intended f(x) to follow a rule - f(x) = x.

Also remember a function is defined by its rule AND its domain.

[Tobias Funke]

what happens when a square root is in the denominator for graphs?

eg. "The Maximal domain of the function with rule f(x)=9/rootx^2-1 is"