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Let f:R to [1,oo),f(x)=x^(2)-4x+5. Then ...

Let `f:R to [1,oo),f(x)=x^(2)-4x+5`. Then find the largest possible intervals for which `f^(-1)(x)` is defined and find corresponding `f^(-1)(x).`

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To solve the problem, we need to find the largest possible intervals for which the inverse function \( f^{-1}(x) \) is defined for the function \( f(x) = x^2 - 4x + 5 \). We will also find the corresponding expressions for \( f^{-1}(x) \). ### Step-by-Step Solution: 1. **Identify the Function**: The given function is \[ f(x) = x^2 - 4x + 5. ...
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