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If the function f(x)=-4e^((1-x)/2)+1+x+(...

If the function `f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)(x),` then the reciprocal of `g^(prime)((-7)/6)` is_________

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The correct Answer is:
5
We have `(gof)(x)=x` or `g^(')(f(x))f^(')(x)=1` when `f(x)=(-7)/6`
`x=1`, or `g^(')((-7)/6)f^(')(1)=1`
Hence `g^(')((-7)/6)=1/(f^(')(1))=1/5`
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