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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+36x−4,x≠23f(x)=\frac{4x+3}{6x-4}, x\neq \frac{2}{3}, then show that (fof) (x)=x(x)=x, for all x≠23x\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+36x−4f(x)=\frac{4x+3}{6x-4}
f∘f(x)=4(4x+36x−4)+36(4x+36x−4)−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+18x−1224x+18−24+16=\frac{16x+12+18x-12}{24x+18-24+16}
=34x34=x=\frac{34x}{34}=x
y=4x+36x−4y=\frac{4x+3}{6x-4}
6xy−4y=4x+36xy-4y=4x+3
6xy−4x=4y+36xy-4x=4y+3
x=4y+36y−4x=\frac{4y+3}{6y-4}
∴f(x)=4x+36x−4\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,b∈Aa, 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,c∈Aa, 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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