how do you do this guys?
Not 100% confident on this one but if the answer is A I can share my working.
sorry i have another question. How do you do part iv, it's one mark but wth :S
i) for an inverse to exist, f(x) must be a one to one function (there must be a unique y-value for every x-value). By restricting the domain to one side of the turning point at x =2 (after which y-values will begin to repeat) we turn f(x) into a one-to-one function, thus an inverse exists for values including and on one side of the point (2,0), in this case x >= 2.
ii) Domain and range of the inverse are the same as the original function, but swapped. This is because (x,y) → (y,x). The range of the inverse becomes [2,∞). The domain will be [0,∞) because that's the range of the original function.
iii) f(x)=f
-1(x) implies that f(x)=x because any intersections between the function and its inverse will occur on the line y=x.
Edit: Make a mistake on this one, fixed it up.
Edit Edit: Make a different mistake that I didn't fix up the first time.
iv) as the inverse function in this case is 2-sqrt(x) because k < 2.