How to find range of a function easilyFind range of x/x^2+1
Saksham , 8 Years ago
Grade 11
Algebra> How to find range of a function easilyFin...
1 Answers
Shahid
The easiest way I Know is to equate the given function[f(x)] to “y”.
For Example......
x/(x2 + 1 ) = y
i.e. x = y(x2 ) + y
i.e. y(x2 ) – x + y = 0
This is a Quadratic Equation in terms of “x”
And as it is understood that “x” is real.... The determinant of this equation must be 
O.....
Therefore (-1)2 – 4(y)(y) 
0
1 – 4y2 0
Thus 4y2 – 1 
0
y2 (1/4)
Therefore.... y
(-∞ , -1/2) 
(1/2 , ∞)
This gives the Range of the given function........ i.e. (-∞ , -1/2) (1/2 , ∞)
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