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.

Answer

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Answer

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

Steps

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: $\boxed{\text{(D) The function is not one-to-one.}}$