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Question
If f(x) = `1/(2x + 1)`, x > `-1/2`, then show that f(f(x)) = `(2x + 1)/(2x + 3)`
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Solution
Given f(x) = `1/(2x + 1)`
f(f(x)) = f`(1/(2x + 1))`
`= 1/(2(1/(2x + 1)) + 1)`
`= 1/(2/(2x + 1) + 1)`
`= 1/((2x + 2 + 1)/(2x + 1))`
`= (2x + 1)/(2x + 3)`
since x ≠ `- 3/2`
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