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Let f: R → R be a one-one onto different...

Let f: `R → R` be a one-one onto differentiable function, such that `f(2)=1 and f^(prime)(2)=3.` Then, find the value of `(d/(dx)(f^(-1)(x)))_(x=1)`

Text Solution

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Let `f^(-1)(x)=g(x)`
`therefore" "f(g(x))=x`
`therefore" "f'(g(x))g'(x)=1`
`therefore" "g'(x)=(1)/(f'(g(x)))`
`therefore" "g'(1)=(1)/(f'(g(1)))=(1)/(f'(2))=(1)/(3)`
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