CBSE Class 12 Math 2020 Delhi Set 1 Solved Paper

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Section - B

Q. Nos. 21 to 26 carry 2 marks each.
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Question : 21 of 36
 
Marks: +1, -0
If f(x)=4x+36x−4,x≠23, then show that (fof) (x)=x, for all x≠23. Also, write inverse of f.
OR
Check if the relation R in the set ℝ of real numbers defined as R={(a,b):a<b} is (i) symmetric, (ii) transitive
Solution:
f(x)=4x+36x−4
f∘f(x)=4(4x+36x−4)+36(4x+36x−4)−4
=16x+12+18x−1224x+18−24+16
=34x34=x
y=4x+36x−4
6xy−4y=4x+3
6xy−4x=4y+3
x=4y+36y−4
∴f(x)=4x+36x−4
OR
Given : R={(a,b):a<b}
Let A be the set of real numbers.
(i) For symmetric : Let a,b∈A
Then, (a,b)∈R such that a<b
⇒b<a which is false
⇒(b,a)∉R
∴R is not symmetric.
(ii) For transitive : Let a,b,c∈A
Then, (a,b)∈R and (b,c)∈R
⇒a<b and b<c
⇒a<c
⇒(a,c)∈R
∴R is transitive.
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