262note that f(pi/2) = pi
thus f-1(pi) = pi/2
thus we only have to find f'(pi/2) = 3
Question:
f(x)=(2x-∩)3 +2x - cosx.
Then the value of |f'(f-1(x))| at x=∩ is _______?
answer: 1/3
I think drawing the graph is only way. Any accurate and easier solution please tell me.
(SOURCE: ARIHANT)
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7 Answers
1i think drawing the graph is the easiest solution
DON'T DRAW IT COMPLETELY
sketch a rough one by putting certain values of x
and an accurate one about x=∩
262
1But aditya, the answer given is 1/3.
And aditya how did you get f'(pi/2) as 3?
1Hey Aditya am so sorry in the question actually we need to find derivative of f-1(x) at x=pi.
So we need |d(f-1(x))/dx| at x = pi.
262f-1(f(x)) = x
diff. w.r.t x ,
(f-1(f(x))) ' * f'(x)= 1
here f(x) = pi
thus x=pi/2
thus (f-1(pi)) ' = 1/f'(pi/2) = 1/3