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Find the domain and range of f(x)=sqrt(3...

Find the domain and range of `f(x)=sqrt(3-2x-x^2)`

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Verified by Experts

The correct Answer is:
Domain: [-3, 1], Range: [0, 2]
`f(x)=sqrt(3-2x-x^(2))` is defined if
`3-2x-x^(2) ge 0`
or `x^(2)+2x-3 le 0`
or `(x-1)(x+3) le 0`
or ` x in [-3,1]`
Also, `f(x)=sqrt(4-(x+1)^(2))` which has maximum value when
`x+1=0.`
Hence, the range is `[0,2].`
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