3 - Set Theory and Relations Questions Answers
number of real values of x satisfying 2log2(x+7x+1)+log2(x+1x-1)=1 is
given eq. can be written as log2 [(x+7)/(x+1)]2 + log2 [(x+1)/(x-1)] = 1
or log2 [(x+7)2(x+1)/(x+1)2(x-1)] = 1
or log2 [(x+7)2/(x2-1)] = 1
or (x+7)2/(x2-1) = 2
or x2 + 14x +49 = 2x2 - 2
or x2-14x -51 = 0
or x = -3, 17
since at x = -3 first part will become negative inside root so it will not be a root.
so only 1 root
The number of solutions of : 4x²-4x+2 = sin² y & x²+y² ≤ 3 are ? (please solve it graphically i am getting one solution by using graph but the answer is 2)
Given eq. can be written as (2x-1)2 + 1 = sin2y
and max. of siny is 1 so only possible value of x = 1/2
and possible values of y = ±nπ/2 where n is odd integer
but by drawing the circle of 2nd eq. we find that only y = ±π/2 are possible values so answer will be 2
What is the range of the function y = (e^-x)/ (1+[x]) is ?
Domain of the given function is (-∞, -1) υ [0, ∞)
Now at x=0, y=1
and at x=∞, y=0
similarly left limiting value of y = -e
and for x=-∞, y=-∞
so range is (-∞, -e] υ (0, 1]