Match the followingList-IList –IIA) f(x)=e2x,g(x)=logx then fog(x)=P) −∞,1∪3,∞B) f(x)=2x−3,g(x)=x3+5 then fog−1(x)Q) 0C) Domain of log x2−4x+3 R)x−721/3D) Range of f(x)=sinπx1+x2. represents G.I.FS)x2

a fogx= fgx=e2logx=elogx2=x2b fx3+5y=2x3+7x3=y−72x =y−721/3x−1x−3>0x∈−∞,1∪3,0d 0

Match the followingList-IList –IIA) f(x)=e2x,g(x)=logx then fog(x)=P) −∞,1∪3,∞B) f(x)=2x−3,g(x)=x3+5 then fog−1(x)Q) 0C) Domain of log x2−4x+3 R)x−721/3D) Range of f(x)=sinπx1+x2. represents G.I.FS)x2

a fogx= fgx=e2logx=elogx2=x2b fx3+5y=2x3+7x3=y−72x =y−721/3x−1x−3>0x∈−∞,1∪3,0d 0

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Match the following
List-I List –II
$A) f (x) = e^{2 x}, g (x) = \log x$ then $(f o g) (x) =$ $P) (- \infty, 1) \cup (3, \infty)$
$B) f (x) = 2 x - 3, g (x) = x^{3} + 5$ then ${(f o g)}^{- 1} (x)$ Q) $\{0\}$
C) Domain of log $(x^{2} - 4 x + 3)$ $R) {(\frac{x - 7}{2})}^{1 / 3}$
D) Range of $f (x) = \frac{\sin π [x]}{1 + {[x]}^{2}}$
$[.]$ represents G.I.F
$S) x^{2}$

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$A \to S, B \to R, C \to Q, D \to P$

$A \to Q, B \to S, C \to R, D \to P$

$A \to S, B \to R, C \to P, D \to Q$

$A \to P, B \to R, C \to S, D \to Q$

answer is C.

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Detailed Solution

$(a) f o g (x) = f [g (x)]$

$= e^{2 \log x} = e^{\log x^{2}} = x^{2}$

$(b) f (x^{3} + 5)$

$y = 2 x^{3} + 7$

$x^{3} = \frac{y - 7}{2}$

$x^{} = {(\frac{y - 7}{2})}^{1 / 3}$

$(x - 1) (x - 3) > 0$

$x \in (- \infty, 1) \cup (3, 0)$

$(d) \{0\}$

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List-I	List –II
$A) f (x) = e^{2 x}, g (x) = \log x$ then $(f o g) (x) =$	$P) (- \infty, 1) \cup (3, \infty)$
$B) f (x) = 2 x - 3, g (x) = x^{3} + 5$ then ${(f o g)}^{- 1} (x)$	Q) $\{0\}$
C) Domain of log $(x^{2} - 4 x + 3)$	$R) {(\frac{x - 7}{2})}^{1 / 3}$
D) Range of $f (x) = \frac{\sin π [x]}{1 + {[x]}^{2}}$ $[.]$ represents G.I.F	$S) x^{2}$

Match the followingList-IList –IIA) f(x)=e2x,g(x)=logx then fog(x)=P) −∞,1∪3,∞B) f(x)=2x−3,g(x)=x3+5 then fog−1(x)Q) 0C) Domain of log x2−4x+3 R)x−721/3D) Range of f(x)=sinπx1+x2. represents G.I.FS)x2

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