Question:
if f(x)=3x-2/2x-3 ,prove that f(f(x) =x...x..R-3/2
Answer:
Given, f(x) = (3x - 2)/(2x - 3)
Now, f(f(x)) = f{(3x - 2)/(2x - 3)}
= {(3*(3x - 2)/(2x - 3) - 2)}/{(2(3x - 2)/(2x - 3) - 3)}
= {(9x - 6)/(2x - 3) - 2)}/{((6x - 4)/(2x - 3) - 3)}
= [{(9x - 6) - 2(2x - 3)}/(2x - 3)]/[{(6x - 4) - 3(2x - 3)}/(2x - 3)]
= {(9x - 6) - 2(2x - 3)}/{(6x - 4) - 3(2x - 3)}
= (9x - 6 - 4x + 6)/(6x - 4 - 6x + 9)
= 5x/5
= x
So, f(f(x)) = x
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