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First work out y² using the second equation, making sure to do this using the FOIL technique. Then substitute this into the first equation to get 5x² - 40x - 80 = 0. All the terms in...

Rewrite as y = 2 / (x^2 + 2). Swap all x and y symbols to create x = 2 / (y^2 + 2). Rearrange for y to reach y=g(x)=sqrt( (2-2x) / x ).

This is an example of differentiation. With differentiation the key rule that allows us to differentiate most algebraic functions is "times the coefficient by the power then decrease the power by one...

Firstly, ff(8) is the same as f(f(8)) so f(8) needs to be found first. Subbing in x=8 f(8)=22/3, so f(22/3) is required, Setting x=22/3 f(22/3)= 20/(22/3 - 5) = 60/7. so ff(8)=60/7.Next, as x tends to in...