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Question
If f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)` then verify that `("fog") (x)` = x.
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Solution
f(x) = `(x+3)/(4x−5) , "g"(x) = (3+5x)/(4x−1)`
`("fog")(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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