I am stuck about two thirds of the way through this question and can't figure the remaining part out.
f(x) = 24x-15 g(x)=2x-d where d is an unknown value, it is known that inverse f(inverse g(x)) = inverse g(inverse f(x))
I have to first of all find the value of d, and secondly find; inverse f(inverse g(20))
We have been using mathCAD to solve similar but I really want to learn how to solve this the "old school" way using a pen and paper!
So far I have got;
inverse f(x) = x/24 - 5/8 inverse g(x) = x/2 + d/2
inverse f(inverse g(x)) = (d/2 +x/2)/24 - 5/8 = d/48 + x/48 - 5/8
inverse g(inverse f(x)) = d/2 + (x/24 - 5/8)/2 = d/2 + x/48 - 5/16
Therefore; d/48 + x/48 - 5/8 = d/2 + x/48 - 5/16
I am now stuck at that point and cannot figure out the next steps. On mathCAD the next step is to (solve, d) and it gives you the answer, and then for the second part of the question you can substitute the values of d and x into the equation(s) to give you the answer.
I have been stuck on this for hours and just cannot get past the final hurdle, please help!! P.s. I do know the answers from mathCAD which are; d = -15/23 and for the second part of the question the answer is -0.222.
Thanks in advance