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Work Done When Force Is Varying

If fx= | x-...

Question

If $f (x) = \frac{| x - 1 |}{x^{2}}$ then $f (x)$ is

A

One - One in

(2, \infty)

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B

One - One in

(0, 1)

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C

One - One in

(- \infty, 0)

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D

One - One in

(1, 2)

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Solution

The correct options are
C One - One in $(- \infty, 0)$
D One - One in $(1, 2)$

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Similar questions

Q. Verify Lagrange's mean value theorem for the following functions on the indicated intervals. In each case find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem
(i) f(x) = x² − 1 on [2, 3]
(ii) f(x) = x³ − 2x² − x + 3 on [0, 1]
(iii) f(x) = x(x −1) on [1, 2]
(iv) f(x) = x² − 3x + 2 on [−1, 2]
(v) f(x) = 2x² − 3x + 1 on [1, 3]
(vi) f(x) = x² − 2x + 4 on [1, 5]
(vii) f(x) = 2x − x² on [0, 1]
(viii) f(x) = (x − 1)(x − 2)(x − 3) on [0, 4]
(ix)

f (x) = \sqrt{25 - x^{2}}

on [−3, 4]
(x) f(x) = tan⁻¹ x on [0, 1]
(xi)

f (x) = x + \frac{1}{x} on [1, 3]

(xii) f(x) = x(x + 4)² on [0, 4]
(xiii)

f (x) = \sqrt{x^{2} - 4} on [2, 4]

(xiv) f(x) = x²+ x − 1 on [0, 4]
(xv) f(x) = sin x − sin 2x − x on [0, π]
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Q. Verify Rolle's theorem for each of the following functions on the indicated intervals
(i) f(x) = x² − 8x + 12 on [2, 6]

(ii) f(x) = x² − 4x + 3 on [1, 3]

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(iv) f(x) = x(x − 1)² on [0, 1]

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Q. Verify Rolle's theorem for each of the following functions on the indicated intervals
(i) f(x) = x² − 8x + 12 on [2, 6]

(ii) f(x) = x² − 4x + 3 on [1, 3]

(iii) f(x) = (x − 1) (x − 2)² on [1, 2]

(iv) f(x) = x(x − 1)² on [0, 1]

(v) f(x) = (x² − 1) (x − 2) on [−1, 2]

(vi) f(x) = x(x − 4)² on the interval [0, 4]

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Q. Find the value of

a

so that the equation

f (x) = x^{2} + (a - 3) x + a = 0

has exactly one root

α

, between the interval

(1, 2)

f (x + α) = 0

has exactly one root between the interval

(0, 1)

$L e t f : [0, \sqrt{3}] \to [0, \frac{π}{3} + l o g_{e} 2] d e f i n e d f (x) = l o g_{e} \sqrt{x^{2} + 1} + t a n^{- 1} x t h e n f (x) i s$

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