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Find all the possible values of f(x) =(1...

Find all the possible values of `f(x) =(1-x^2)/(x^2+3)`

Text Solution

Verified by Experts

The correct Answer is:
`y in (-1, 1//3 ]`
f(x)=y=`(1-x^2)/(x^2+3)`
or `yx^2+3y=1-x^2`
`or yx^2+3y=1-x^2`
`or x^2=(1-3y)/(y+1)`
Now `x^2 le 0 `
`rArr (1-3y)/(y+1) ge 0`
`rArr (3y-1)/(y+1) le 0 `
`rArr (3y -1)/(y+1) le 0 `
Hence `y in (-1 , 1//3]`
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