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Your working is fine except that one part. If you actually tried to answer my question you will be able to understand why.

You won't learn if I just spoonfeed you the answer. In the bolded part, why did you pick only the positive square root? Why did you ignore/reject the negative square root?

When you took the square root, why did you choose the positive and not the negative one? Think about which one makes sense given the condition imposed.

Yes. That question you managed to answer yourself, what was the problem you had with it originally that prompted you to ask it?

Bump

Ok let's start with f(x)=(x-2)2 for x < 2. What did you get for the inverse function f-1(x)?

Can you please answer my question?

So what was the problem you had with the question originally?

Ok now do you know how to find the domain and range of the inverse?

Ok now do you know how to find the domain and range of the original function?

The fact that you don't know how to make x the subject and want to do 4U is a little concerning

Ok lets start with y=8(x-1)3 You said earlier to swap the x and y to find the inverse function. Do you know how to do that for y=8(x-1)3? Also do you know how to find the domain and range of that function?

Have you looked through your notes or textbook again to see how to sketch it? Okay, so using that information what is the equation of the inverse function of y=-ln(x+1)? Have you looked through your notes or textbook again to see what that important graphical relationship is?

Do you know how to sketch a log graph in the first place? Also do you know how to find the equation of an inverse function? Do you know the relationship between the graph of a function and a graph of its inverse?

I'm assuming you mean assessments other than trials? There is no rule. I've had practical assessments for my science subjects in the same week as my trials.

You got the question wrong. Assume that for some n=k \frac{1}{x^k(x-1)}=\frac{1}{x-1}-\frac{1}{x}-\frac{1}{x^2}-.........-\frac{1}{x^k} Now we can show that...

Is this from tutor? What topics have you already done at school (or tutor for that matter)? This isn't exactly prelim stuff.

Re: University Statistics Discussion Marathon This is needed if there is a sampling without replacement which I guess now looking at the question again is somewhat implied but not immediately obvious. If it is a sampling with replacement then what I had earlier is correct.

Re: University Statistics Discussion Marathon $Since $X\sim N(100,100)$ then $\bar{X}\sim N\left(100,\frac{100}{50}\right)$ so $\\\\P(\bar{X} > 103)\\\\=P\left(\dfrac{\bar{X}-100}{\sqrt{\frac{100}{50}}}>\dfrac{103-100}{\sqrt{\frac{100}{50}}}\right)\\\\=P\left(Z> \dfrac{3}{\sqrt{2}}\right)\:$...

For Q19 note that the break even point is where consumption equals income so substitute C=Y into the consumption function (which is equivalent to finding the intersection of the 45 degree line and the consumption function).