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 \(g(g(g(10.5)))=g(g(g(a)))\) .

Havingfun Apr 26, 2019

#2**+2 **

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

Melody Apr 27, 2019