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Find the range of function `y=ln(2 x-x^(2))`

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Find the range of function `y=ln(2 x-x^(2))`
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Step-1
We have `2x-x^(2)epsilon(-oo,1]`
Step -2 Let `t=2x-x^(2)`
for `lnt` to be defined accepted values are `(0,1]`
Now, using monotonicity of `lnt`,
`ln(2x-x^(2))epsilon(-oo,0]`
`:.` range is `(-oo,0]`
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