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f(x)=x/2x-1 f(g(x))=x+1/1-x find g(x)
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let, `f(x) = x/(2x-1)` and `f(g(x)) = (x+1)/(1-x)`
Suppose g(x) = y then,
`f(g(x)) = y/(2y-1)`
But we know `f(g(x)) = (x+1)/(1-x)` , therefore,
`(x+1)/(1-x) = y/(2y-1)`
By solving this for y, we can find g(x).
Rearranging above equation would give us,
`(2y-1)(x+1) = y(1-x)`
`2y-1+2xy-x = y -xy`
`y = (x+1)/(1+3x)`
Therefore, `g(x) = (x+1)/(1+3x)`
Posted by thilina-g on May 9, 2012 at 6:46 AM (Answer #1)
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