If f(x) = 2x + 3, & g(x) = (x - 3)/2, then what is the value of, fo(fo(go(go(fo(fo(go(go................(fo(fo(go(gof(x) )))).....)))))) ?	Choices
A) 3 B) 2 C) 9 D) 7 E) 1

Rationale: f ( x ) = 2 x + 3 g ( x ) = ( x - 3 ) / 2 gof ( x ) = 2 x + 3 − 32 = x 2 x + 3 − 32 = x gogof ( x ) = x − 32 x − 32 fogogof ( x ) = 2 ( x − 32 ) + 32 ( x − 32 ) + 3 = 2 x − 6 + 622 x − 6 + 62 = x fofogogof ( x ) = 2 x + 3 this means , when we apply two times g ( x ) and two time f ( x ) on f ( x ) we get f ( x ) . this pattern continues , hence the answer is option ( d ) .
Answer: D