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Let fa n dg be real functions defined by...

Let `fa n dg` be real functions defined by `f(x)=x/(x+1)a n dg(x)=1/(x+3)dot` Describe the functions `gofa n dfog` (if they exist).

Text Solution

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`(f o g)^{-1}(x)=(g^{-1} 0 f^{-1})(x)`
` Since, f(x)=x+1, y=x+1`
` x y+y=x`
` x(1-y)=y`
` x=y /[1-y] `
` f^{-1}(y)=y /[1-y] `
` f^{-1}(x)=x /[1-x] `
` Let z=g(x)=x /[1-x] `
` ...
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