InterviewSolution
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InterviewSolution
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Find the number of ordered pairs (a, b) from the set A = {1,2,3,4,5) so that the functionf(x)=3+2x2+bx + 10 YxeRis an injective mapping |
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Answer» put the values in equationX=1(1)^3/3+a/2(1)^2+b(1)+101/3+a/2+b+10X=22^3/3+a/2*2^2+2b+108/3+4a/2+2b+10for injective mapping the above two equations should be equalhence 1/3+a/2+b+10=8/3+2a+2b+101/3-8/3=2a+2b-a/2-b-7/3=3a/2-b----1similarly put x=3 and X=4X=33^3/3+a(3)^2/2+3b+109+9/2a+3b+10and X=44^3/3+a(4)^2/2+4b+10equate these two equations9+9/2a+3b+10=64/3+8a+4b 9-64/3=8a-9/2a+4b-3b27-64/3=16-9/2a+b-37/3=7/2a+b----2now solving 1 and 2add the two equations-44/3=5aa=-44/15now put in equation 1-7/3=3*(-44/15)-b-7/3=-44/5-bb=-44/5+7/3b=-132+35/15b=-98/15 |
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