Mixed questions [Functions and Sequenzes & Series]

[Calavera]

Hi there,
I have a math test tomorrow and I have some questions from our books review sets that I haven't been able to solve yet. For now I only have questions on functions and Sequenzes & Series but it's possible that I might ad a few more later during the day. Here it goes...
---Functions---
1) I have the folowing graph, and with its help I'm supposed to find the domain and range. I can easily find the domain, but not the range. I don't actually know how to do it...
http://www.viitanen.se/q1f.gif
2) I plot the graph g(x)=x^2 + 6x + 7
Then I'm supposed to: "explain why g for x ≤ -3 has an inverse function g^-1".
To be honest I don't even know how to start...
3) Given h(x)=(x-4)^2 +3 where x≥3 I'm supposed to find the defining equation of h^-1.
I started on this by chaning the variables (changin place with y and x), and I finaly got it to: y^2 - 8y +16 = x-3. Ok, I can simplyfy it more but what should I do to the y^2? Should I use the abc formula, should I factorize it?
---Sequences & series---
1) Find the first term of the sequence 5, 10, 20, 40 which exceeds 10 000.
I wrote up the formula (5(2^n -1))/1 and plotted it on my gdc, then I got the answer that it was supposed to be U11, and when I put that into my formula and I got a right answer, 10235. The thing is that the key to the book says: "t12=10240"!
2)6000€ is invested, at 7% p.a. What is the compound interest after 5 years if the interest is compounded a) quaterly b) monthly.
I have really tried to solve this several times but haven't succeded. I don't simply know what to do...please help.
Ok, I know that there are a lot of problems but I would be really happy if someone could help me...soon if possible (test tomorrow). Thank you in advance!

 

[Kamataat]

For #2, what condition must a function meet for an inverse to exist? Does g meet this condition for x <= -3?

edit: sign error

- Kamataat

 

[Calavera]

A inverse has to be reflected in the line Y=X and it has to pass the horizontal line test ie only have one possible x value for each y value??
How am I supposed to know if g meets the condition?

 

[Fermat]

Functions
1) what is the min value y can have ?
What is the max value y can have ?
The difference gives you the range of y.

3) don’t square out the (y-4) term. Instead take the square root of the other term (put a square root sign over it) and find y.

Sequences and Series
1) Did you notice that your answer and the book’s answer were out by 5, which is the value of your first term ?
Your expression for the nth term was out. You had U_n = 5(2ⁿ – 1). It should have been U_n = 5(2^n-1)

2) the formula needed for compound interest is,

P_n = P₀(1 + a)ⁿ

Where P₀ is the original principle,
P_n is the principle after n intervals of getting interest added,
a is the interest rate for one particular time interval,
n is the number of time intervals.

You have two time intervals of interest. Monthly and quarterly. Get the right value of a for each time interval.

 

[Kamataat]

A inverse has to be reflected in the line Y=X and it has to pass the horizontal line test ie only have one possible x value for each y value??
How am I supposed to know if g meets the condition?

The function is strictly decreasing for x < -3.

- Kamataat