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How do you graph |z-1/z|=2?

So we are looking for domain of f(g(x)), x values of g only makes sense if x values are within 1 to 4. then f takes the y values of g as its x values, which means f takes values between [2,6] but domain of f is [0,5], so surely that means f takes values from 2 to 5? so I'm not sure how you are...

hmm i tried a few times still not sure how to do it, don't we find the domain of g(x) and intersect with domain of f(g(x))?

What is the answer you are getting?

Can anyone provide the working for below? Tysm

how do we do the last two?

wow this is a genius at work! and your from year 12?

thanks so much! cant believe they ask this in year 8 SCHOOL EXAM at my school! Are you able to help with the first question plz?

hmm seems this question is slightly harder though coz it cant be factorised?

can anyone help?

right, so could you shed some light on how to solve the above questions?

and another similar one... Q: positive integers x and y satisfy the equation 3x+5y=2xy-1, find all possible values of x-y.

I'm always getting stuck with questions like these, not in standard textbooks i don't think, how can i improve on these, like any books out there or website?(and also if you can shed light on how to solve it plz...) Q: Determine all possible pairs of positive integers such that their sum is 2623...

Was just trying out a few things with first principles and got stuck at one point: \lim_{x\to 0} \cfrac{\sqrt{x^2+x^3}}{x} can someone help?

damn...this is tough, can anyone help?

I am fine for the first part, not sure how to do the HENCE part...it could have been easily done with letting f(x)=e^x-1-a^2 and showing its always positive...but the HENCE...

Hmm I fail to see how this hint helps with part (ii), are we talking about the same Sphere question that's on this page? Do you happen to have the link for the nesa sample link?

can anyone help?

also 5u, in this solution of yours you mentioned use part (i), what is part (i)?