Problem

If $f$ is one-to-one, find an equation for its inverse. \[ f(x)=(x-3)^{2} \] A. $f^{-1}(x)=\sqrt{x}+3$ B. $f^{-1}(x)=\sqrt{x+3}$ $f^{-1}(x)=\frac{1}{\sqrt{x+3}}$ D. The function is not one-to-one.

Solution

Step 1 :The function \(f(x)=(x-3)^{2}\) is not one-to-one because for any given \(x\) value, there are two possible \(y\) values.

Step 2 :For example, if \(x=4\), then \(y=(4-3)^{2}=1\), but if \(x=2\), then \(y=(2-3)^{2}=1\) as well.

Step 3 :Therefore, the function does not have an inverse.

Step 4 :Final Answer: \(\boxed{\text{(D) The function is not one-to-one.}}\)

From Solvely APP
Source: https://solvelyapp.com/problems/19049/

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