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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 ` x^(2)=(1-3y)/(y+1)`
Now `x^(2) ge 0`

`implies (1-3y)/(y+1) ge 0`
`implies (3y-1)/(y+1) le 0`
Hence, `y in (-1,1//3]`
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