Question

How so I solve this? `2-(x+1)^(1/2)-x^2+4x-3 , 0<x<1`

Answer 1

`-2<2-(x+1)^(1/2)-x^2+4x-3<2-sqrt2`

Explanation:

If you meant what `2-(x+1)^(1/2)-x^2+4x-3` is between, then this solution is for you.

So, since `x` is a number greater than 0, we plug in 0 to the expression to get:
`2-(0+1)^(1/2)-0^2+4(0)-3`
`2-(1)^(1/2)-0+4(0)-3`
`2-1-0+0-3`
`-2`
This means that `2-(x+1)^(1/2)-x^2+4x-3` has to be greater than `-2`

Similarly, since `x` is a number smaller than 1, we plug in 1 to the expression to get:
`2-(1+1)^(1/2)-1^2+4(1)-3`
`2-(2)^(1/2)-1+4(1)-3`
`2-(2)^(1/2)-1+4-3`
`2-sqrt2`
Which is approximately `0.585786437627`. Therefore, `2-(x+1)^(1/2)-x^2+4x-3` has to be less than `2-sqrt2`

So we now have :`-2<2-(x+1)^(1/2)-x^2+4x-3<2-sqrt2`