Q. 65.0( 4 Votes )
Let g(x) be the inverse of an invertible function f(x) which is derivable at x = 3. If f(3) = 9 and f’(3) = 9, write the value of g’(9).
Answer :
From the definition of invertible function,
g(f(x)) = x …(i)
So, g(f(3)) = 3, i.e., g(9) = 3
Now, differentiating both sides of equation (i) w.r.t. x using the Chain Rule of Differentiation, we get –
g’(f(x)). f’(x) = 1 …(ii)
Plugging in x = 3 in equation (ii) gives us –
g’(f(3)).f’(3) = 1
or, g’(9).9 = 1
i.e., g’(9) = 1/9 (Ans)
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