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If f(x)=x^{2}-x+5,x>\frac{1}{2} and g(x) is its inverse function,then  g'(7)   equals:

Option: 1

-\frac{1}{3}


Option: 2

\frac{1}{13}


Option: 3

\frac{1}{3}


Option: 4

-\frac{1}{13}


Answers (1)

best_answer

Given that, g(x) is inverse of f(x)

\\g\left ( f(x) \right )=x\\\text{differentiate both side}\\ g'(f(x))\cdot f'(x)=1\\

we need to find g'(7), so f(x) =7

now,

 \\f(x)=x^2-x+5=7\\x=-1\:\:or\:\:x=2\\since,\:x>\frac{1}{2},\:so,\:\:x=2

\\f'(x)=2x-1\\g'(7)\cdot f'(x)=1\\g'(7)=\frac{1}{2x-1}\\\text{put x = 2} \\g'(7)=\frac{1}{3}

 

 

Posted by

avinash.dongre

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