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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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Verified by Experts

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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  2. If y=f(x) is an odd differentiable function defined on (-oo,oo) such t...

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  6. y=f(x) , where f satisfies the relation f(x+y)=2f(x)+x y(y)+ysqrt(f(x)...

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  7. If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f...

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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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  12. A nonzero polynomial with real coefficient has the property that f(x)=...

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  14. Let z=(cosx)hat5a n dy="sin"xdot Then the value of 2(d^2z)/(dy^2)a tx=...

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  15. Let g(x)={(x^2+xtanx-xtan2x)/(a x+tanx-tan3x),x!=0 0,x=0 If g^(prime)...

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  16. Let f(x)=x+1/(2x+1/(2x+1/(2x+oo))) Compute the value of f(50)dotf^(p...

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  17. Let F(x)=f(x)g(x)h(x) for all real x ,w h e r ef(x),g(x),a n dh(x) are...

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  18. "If "y=(root(3)(1+3x)root(4)(1+4x)root(5)(1+5x))/(root(7)(1+7x)root(8)...

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

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