Fx-x-1x- then f1x-I- fxII- f-xIII- -fxIV- 1fx

The correct option is B II and III f(x)=x 1x f(1x)=1x x (substituting 1x at the place of x) = (x 1x) = f(x) f(1x)=1x x = ( 1 ...

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Byju's Answer

Standard XII

Mathematics

Definition of Functions

fx=x-1x, then...

Question

$f (x) = x - \frac{1}{x}$ , then $f (\frac{1}{x}) =$
I. $f (x)$
II. $f (- x)$
III. $- f (x)$
IV. $\frac{1}{f (x)}$

I and II

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II and III

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III and IV

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II only

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II and IV

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Solution

The correct option is B II and III
$f (x) = x - \frac{1}{x}$
$f (\frac{1}{x}) = \frac{1}{x} - x$ (substituting $\frac{1}{x}$ at the place of x)
$= - (x - \frac{1}{x})$
$= - f (x)$

$f (\frac{1}{x}) = \frac{1}{x} - x$
$= - (- \frac{1}{x}) + (- x) = f (- x)$
$∴ I I$ & $I I I$ .

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f(x)=x−1x, then f(1x)=I. f(x)II. f(−x)III. −f(x)IV. 1f(x)

The correct option is B II and IIIf(x)=x−1xf(1x)=1x−x (substituting 1x at the place of x)=−(x−1x)=−f(x)f(1x)=1x−x=−(−1x)+(−x)=f(−x)∴II & III.

$f (x) = x - \frac{1}{x}$ , then $f (\frac{1}{x}) =$
I. $f (x)$
II. $f (- x)$
III. $- f (x)$
IV. $\frac{1}{f (x)}$

The correct option is B II and III
$f (x) = x - \frac{1}{x}$
$f (\frac{1}{x}) = \frac{1}{x} - x$ (substituting $\frac{1}{x}$ at the place of x)
$= - (x - \frac{1}{x})$
$= - f (x)$

$f (\frac{1}{x}) = \frac{1}{x} - x$
$= - (- \frac{1}{x}) + (- x) = f (- x)$
$∴ I I$ & $I I I$ .