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Question
Answer the following:
If f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)` then show that (f ° g) (x) = x
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Solution
f(x) = `(x + 3)/(4x - 5)`, g(x) = `(3 + 5x)/(4x - 1)`
(f ° g) (x) = f(g(x))
= `"f"((3 + 5x)/(4x - 1))`
= `((3 + 5x)/(4x - 1) + 3)/(4((3 + 5x)/(4x - 1)) - 5)`
= `(3 + 5x + 12x - 3)/(12 + 20x - 20x + 5)`
= `(17x)/17`
= x
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