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CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

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Section - B
Q. Nos. 21 to 26\boxed{26} carry 2\boxed{2} marks each.
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Question : 21 of 36
Marks: +1, -0
If f(x)=4x+36x4,x23f(x)=\frac{4x+3}{6x-4}, x\neq \frac{2}{3}, then show that (fof) (x)=x(x)=x, for all x23x\neq \frac{2}{3}. Also, write inverse of ff.
OR
Check if the relation RR in the set R\mathbb{R} of real numbers defined as R={(a,b):a<b}R=\{(a,b): a < b\} is (i) symmetric, (ii) transitive
f(x)=4x+36x4f(x)=\frac{4x+3}{6x-4}
ff(x)=4(4x+36x4)+36(4x+36x4)4f \circ f(x)=\frac{4\left(\frac{4x+3}{6x-4}\right)+3}{6\left(\frac{4x+3}{6x-4}\right)-4}
=16x+12+18x1224x+1824+16=\frac{16x+12+18x-12}{24x+18-24+16}
=34x34=x=\frac{34x}{34}=x
y=4x+36x4y=\frac{4x+3}{6x-4}
6xy4y=4x+36xy-4y=4x+3
6xy4x=4y+36xy-4x=4y+3
x=4y+36y4x=\frac{4y+3}{6y-4}
f(x)=4x+36x4\therefore f(x)=\frac{4x+3}{6x-4}
OR
Given : R={(a,b):a<b}R=\{(a,b): a < b\}
Let AA be the set of real numbers.
(i) For symmetric : Let a,bAa, b \in A
Then, (a,b)R(a,b) \in R such that a<ba < b
b<a\Rightarrow b < a which is false
(b,a)R\Rightarrow (b,a) \notin R
R\therefore R is not symmetric.
(ii) For transitive : Let a,b,cAa, b, c \in A
Then, (a,b)R(a,b) \in R and (b,c)boR(b,c) \in \text{bo} R
a<b and b<c\Rightarrow a < b \text{ and } b < c
a<c\Rightarrow a < c
(a,c)R\Rightarrow (a,c) \in R
R\therefore R is transitive.
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