SOLUTION: 8. If f(x)= (ax-b)/c and f(f(x))=x for all x, then which of the following must be true? I. |a| = |c| II. a = 0 III. b>0 Answer. I and II only The book has the solution but I c

Question 40413: 8. If f(x)= (ax-b)/c and f(f(x))=x for all x, then which of the following must be true?
I. |a| = |c|
II. a = 0
III. b>0
Answer. I and II only
The book has the solution but I can't seem to understand. Perhaps u can explain it in another way? thank u
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Polynomials-and-rational-expressions/40413 (2006-06-02 00:44:45): 8. If f(x)= (ax-b)/c and f(f(x))=x for all x, then which of the following must be true?
I. |a| = |c|
II. a = 0
III. b>0
Answer. I and II only
The book has the solution but I can't seem to understand. Perhaps u can explain it in another way? thank u
0 solutions
LET F(X)=Y=(AX-B)/C
SO�F(F(X))=F(Y)=(AY-B)/C=X
CX=AY-B=A(AX-B)/C -B = (A^2X-AB-BC)/C
C^2X=A^2X-AB-BC�..FOR THIS TO BE TRUE FOR ALL VALUES OF X ,IT SHOULD BE AN IDENTITY..HENCE COEFFICIENTS OF CORRESPONDING TERMS ARE EQUAL
COEFF.OF X =C^2=A^2��.C=+ OR -A OR �|A|=|C|
CONSTANT TERM =0=-AB-BC=-B(A+C)��.B=0 OR A=-C
SO THE ANSWER IS A=-C�OR��B=0&|A|=|C|
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