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Grade 11IIT JEE Entrance Exam

Find the range of
1/(x^2-x-1) .
Please do answer this question.This is from the Relations and Functions in the book Cengage mathematics for jee mains
.

Question image for Find the range of 1/(x^2-x-1) . Please do answer
Profile image of Kannan
4 Years agoGrade 11
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1 Answer

Profile image of Kuldeepak Dhar Dwivedi
4 Years ago
let y=1/(x²-x-1)
=>yx²-yx-y=1
=>yx²-yc-y-1=0
now
 if y is not equal to zero:
as x is real thus determinant of the function in terms of x must be greater than 0,
thus y²-4(y)(-y-1)≥0
=>y(y-4(-y-1))≥0 
=>Y(5y+4)≥0
=> Y belongs to (-infinity,-4/5]u(0, infinity)
Y=0 is not possible as for that denominator must be infinity but that will make the equation undefined
 thus, its range is (-infinity,-4/5]u(0, infinity)

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