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Let f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2...

Let `f(x)=-4.sqrt(e^(1-x))+1+x+(x^(2))/(2)+(x^(3))/(3)`. If g(x) is inverse of `f(x)` then the value of `(1)/(g^(')(-(7)/(6)))` is

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The correct Answer is:
5
`g(f(x))=x`
`impliesg^(')(f(x))f'(x)=1`
put `f(x)=-(7)/(6)` i.e., `x=1`
`f(x)=-(7)/(6)` `x=1`
`becauseg^(')(-(7)/(6))=(1)/(5)`
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