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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 .

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
Grade:11

1 Answers

Kuldeepak Dhar Dwivedi
14 Points
one month 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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