Question:
If f (x) =3x-2/2x-3, prove that f (f (x ))=x belongs to R-(3/2)
Answer:
Given f(x) = (3x - 2)/(2x - 3)
Now, f(f(x)) = {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)}/{(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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