lf $f (x) = x - x^{2} + x^{3} - x^{4} + \dots . . \infty$ when $| x | < 1$ , then the ascending order of the following is
a) $f (1 / 2)$
b) $f^{- 1} (1 / 2)$
c) $f (- 1 / 2)$
d) $f^{- 1} (- 1 / 2)$

a, b, c, d

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c, d, a, b

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b, a, d, c

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d, c, a, b

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Solution

The correct option is B c, d, a, b
$f (x) = x - x^{2} + x^{3} - x^{4}$
$f (x) = \frac{x}{1 + x} (x) < 1$
$f (\frac{1}{2}) = \frac{1}{3}$
$f (\frac{- 1}{2}) = - 1$
$f (x) = \frac{x}{1 + x}$
$y = \frac{x}{1 + x}$
$y + x y = x$
$\frac{y}{(u - 1)} = x$
$f^{- 1} x = \frac{- x}{x - 1}$
$f^{- 1} (\frac{1}{2}) = 1$
$f^{- 1} (\frac{- 1}{2}) = \frac{- 1}{3}$

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