Well first thing is to find where the domain of f is positve, while here, i'd find the range as well.
Then find the inverse of f.
Have a go at that.
Just a quick question because I can't quite seem to figure this out.
They give you the equation f(x) = 1/6 [x^2 -4x +24].
They then ask you to give the inverse function f-1(x) for which the domain is positive.
It is then given that N is a negative real number not in the domain of f-1(x), asking you to find f-1(f(x)). I sub in the value for f(N) into f(x) then sub that back into f-1(f(x)) but it obviously just gives the number N :S.
Just wondering how people here would approach this question.
The answers give the answer as 4-N :S.
Thanks in advance .
Well I managed to get the domain and range with f-1(x), x>=10/3, y>=2.
the inverse function comes out f-1(x) = 2 + (6x - 20)^1/2.
Both intersect at 4,4 and 6,6.
the problem is that subbing in f(n) into f-1(n) just gives n, but the question asks for n being a negative number not in the domain, and it's answer isn't just n :S.
Since and are mutually inverse, their graphs are symmetric w.r.t. the diagonal line y = x. Suppose that A has the coordinates (N,0). Calculate the coordinates of B, C, D, E and F taking into account that the red parabola is symmetric w.r.t. x = 2 and CD = DE. The y-coordinate of F is .