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Let f: RvecR be a one-one onto different...

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

Text Solution

Verified by Experts

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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