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Question
Answer the following:
If f(x) = `(2x - 1)/(5x - 2), x ≠ 5/2` show that (f ° f) (x) = x
Solution
(f ° f) (x) = f[f(x)]
= `"f"[(2x - 1)/(5x - 2)]`
= `(2((2x - 1)/(5x - 2)) - 1)/(5((2x - 1)/(5x - 2)) - 2)`
= `(2(2x - 1) - (5x - 2))/(5(2x - 1) - 2(5x - 2)`
= `(4x - 2 - 5x + 2)/(10x - 5 - 10x + 4)`
= `(-x)/(-1)`
= x
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