VCE Methods Question Thread!

[Lejn]

Can someone please run me through how to find the domain for this function:

f: R\{0} over R where f(x) = ln(|x|)
g: (-inf, -2.5) over R where g(x) = 2x + 5
Find the domain of f(g(x)).

I always seem to get these wrong, so help is appreciated. Thanks.

Okay, so the first things first, g(x) is on the inside, so the starting limitations are (-inf,-2.5).

We also need g(x) to have a range contained within Ln(|x|)'s domain, or else we won't be able to compute some values. Ln(|x|) allows every value except for zero, meaning that g(x)≠0. When g(x)=0, x = -2.5, so that can't be apart of our domain. It isn't anyway, and so our domain remains (-inf,-2.5).

[ahat]

Okay, so the first things first, g(x) is on the inside, so the starting limitations are (-inf,-2.5).

We also need g(x) to have a range contained within Ln(|x|)'s domain, or else we won't be able to compute some values. Ln(|x|) allows every value except for zero, meaning that g(x)≠0. When g(x)=0, x = -2.5, so that can't be apart of our domain. It isn't anyway, and so our domain remains (-inf,-2.5).

That's what I thought! The answer has this though:
(-inf, 0)\{-2.5}
i.e. It's R- excluding -2.5!

EDIT: Q and A attached

Which is correct, can someone please confirm?

[lzxnl]

The "answers" are wrong. I agree with (-inf, 2.5)
Anything above 2.5 is not part of the original domain of 2x+5=g(x)

[Stevensmay]

That's what I thought! The answer has this though:
(-inf, 0)\{-2.5}
i.e. It's R- excluding -2.5!

Which is correct, can someone please confirm?

Just a heads up as well, you can answer these types of questions on your CAS, TI nspire at least.
I know this is most likely an Ex 1 question but still.

If you define both functions with their domains and then do domain(f(g(x)),x) it returns

[ahat]

Alright, thanks guys
One last question for the night, has anyone got any tips for approaching conditional probability, or probability in general? Any nifty tricks they've picked up, e.g. how to identify a condition etc.? Share your wisdom!

[Rectophobia]

To identify conditional probability, look out for phrases like "given that", "if", "when it is known"

[Henreezy]

To identify conditional probability, look out for phrases like "given that", "if", "when it is known"

Ah yes, nothing like good bed time advice.
Thanks!!

I'd wish you all good luck, but that is everyone's luck.
Kill the exam tomorrow, I know we all can.

[sasa]

Thanks for your patience Henreezy. Best of luck to you, I know you'll kill it.

[Damoz.G]

Good Luck everyone! I'm sure we'll be fine and will nail this Exam (and of course Exam 2 as well)!

[BigAl]

May dx be with you all the time and +c if necessary

[Damoz.G]

May dx be with you all the time and +c if necessary

ROFL! You just made my night!

[sasa]

Moi aussi 

[papertowns]

Just a general maths question! How do I expand square roots in a bracket? e.g. (2rt2 - 2)^2

[Zealous]

Then foil it!

(... or expand like you would normally):

Spoiler

[Damoz.G]

Then foil it (... or expand like you would normally):

WOW! I love the background sound in that YouTube clip.  ;D