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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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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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CENGAGE-DIFFERENTIATION-Exercise (Numerical)
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  7. If function f satisfies the relation f(x)xf^(prime)(-x)=f(-x)xf^(prime...

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  8. If y=(a+b x^(3/2))/(x^(5/4))a n dy^(prime)=0a tx=5, then the value o...

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  10. If the function f(x)=-4e^((1-x)/2)+1+x+(x^2)/2+(x^3)/3a n dg(x)=f^(-1)...

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  11. Suppose that f(0)=0a n df^(prime)(0)=2, and let g(x)=f(-x+f(f(x)))dot ...

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  19. Let y be an implicit function of x defined by x^(2x)-2x^xcot y-1=0....

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