Let \(g(x)\) be a function piecewise defined as \(g(x) = \left\{ \begin{array}{cl} -x & x\le 0, \\ 2x-41 & x>0. \end{array} \right.\)If \(a\)is negative, find \(a\) so that \(g(g(g(10.5)))=g(g(g(a)))\) .
Thanks Alan
I find these difficult to get my head around too.
I find it easier if I draw a graph and I can see what I am doing visually.
g(10.5)=-20
g(-20)=20
g(20)=-1
Now going backwards.
g(what)=20 there are two answers, -20 and 30.5 (this is easy to see from the graph)
so
g(-20)=20 and g(30.5)=20
now go backwards again
g(what)=-20 and g(what)=30.5 looking at the graph I can see that
g(10.5)=-20 and g(-30.5)=30.5 and g(35.75)=30.5
so
g(10.5) is what we started with
You are told that a is negative so 35.75 is no good
a=-30.5
check
g(-30.5)=30.5
g(30.5)=20
g(20)=-1 = g(g(g(10.5)))
ie
g(g(g(-30.5)=g(g(g(10.5)))
a=-30.5