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Flag IIT JEE Entrance Exam> Find the range of 1/(x^2-x-1) . Please do...
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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
.

Kannan , 3 Years ago
Grade 11
anser 1 Answers
Kuldeepak Dhar Dwivedi

Last Activity: 3 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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