If f x - left begin matrix x - 2- - when - X -0 1x- - when 0 x1lendmatrix right-lFind- i f 1-2ii f -2iii f 1iv f -3v f -3

We have, f(x) = { x^2, when x lt; 0 x, when 0 ≤ x lt; 1 1/x, when x gt;1 . (i) f ( 1/2 ) = 1/2 (ii) f( 2) = ( 2)^2 = 4 (iii) f(1) = 1/1=1 (iv) f(√ ...

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Standard XII

Mathematics

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If f x =⟨ lef...

Question

If $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x^{2}, w h e n x < 0 x, w h e n 0 \leq x < 1 \frac{1}{x}, w h e n x > 1 \end{matrix}$
Find: (i) $f (\frac{1}{2})$
(ii) $f (- 2)$
(iii) $f (1)$
(iv) $f (\sqrt{3})$
(v) $f (\sqrt{- 3})$

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Solution

We have,
$f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x^{2}, w h e n x < 0 x, w h e n 0 \leq x < 1 \frac{1}{x}, w h e n x > 1 \end{matrix}$
(i) $f (\frac{1}{2}) = \frac{1}{2}$
(ii) $f (- 2) = (- 2)^{2} = 4$
(iii) $f (1) = \frac{1}{1} = 1$
(iv) $f (\sqrt{3}) = \frac{1}{\sqrt{3}}$
(v) $f (\sqrt{- 3}) =$ does not exist because $\sqrt{- 3} ϵ$ domain (f).

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If f(x)=⎧⎪ ⎪⎨⎪ ⎪⎩x2, when x<0x, when 0≤x<11x, when x>1 Find: (i) f(12) (ii) f(−2) (iii) f(1) (iv) f(√3) (v) f(√−3)

We have, f(x)=⎧⎪ ⎪⎨⎪ ⎪⎩x2, when x<0x, when 0≤x<11x, when x>1 (i) f(12)=12 (ii) f(−2)=(−2)2=4 (iii) f(1)=11=1 (iv) f(√3)=1√3 (v) f(√−3)= does not exist because √−3ϵ domain (f).

If $f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} x^{2}, w h e n x < 0 x, w h e n 0 \leq x < 1 \frac{1}{x}, w h e n x > 1 \end{matrix}$
Find: (i) $f (\frac{1}{2})$
(ii) $f (- 2)$
(iii) $f (1)$
(iv) $f (\sqrt{3})$
(v) $f (\sqrt{- 3})$