Determine the inverse of $y(x)=(x+1)^2$, $(x\geq 0)$.
Antwoord 1 correct
Fout
Antwoord 2 optie
$x(y)=\sqrt{y}-1$
Antwoord 2 correct
Fout
Antwoord 3 optie
$x(y)=\sqrt{y} +1$
Antwoord 3 correct
Fout
Antwoord 4 optie
None of the other answers are correct.
Antwoord 4 correct
Correct
Antwoord 1 optie
This inverse does not exist.
Antwoord 1 feedback
Wrong: Due to the domain the equation $y=(x+1)^2$ has only one solution for every $y\geq 1$.
Try again.
Try again.
Antwoord 2 feedback
Wrong: What happens if $y=0$?
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Try again.
Antwoord 3 feedback
Wrong: Consider the minus-sign.
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Try again.
Antwoord 4 feedback
Correct: We rewrite:
$$\begin{align*}
y=(x+1)^2 & \Leftrightarrow \sqrt{y}=x+1\\
& \Leftrightarrow x+1=\sqrt{y}\\
& \Leftrightarrow x=\sqrt{y}-1.
\end{align*}$$
Hence, the correct answer is $x(y)=\sqrt{y}-1$, $(y\geq 1)$. The domain is crucial here, as the domain of $x$ is $x\geq 0$, and this only holds for $y\geq 1$.
Go on.
$$\begin{align*}
y=(x+1)^2 & \Leftrightarrow \sqrt{y}=x+1\\
& \Leftrightarrow x+1=\sqrt{y}\\
& \Leftrightarrow x=\sqrt{y}-1.
\end{align*}$$
Hence, the correct answer is $x(y)=\sqrt{y}-1$, $(y\geq 1)$. The domain is crucial here, as the domain of $x$ is $x\geq 0$, and this only holds for $y\geq 1$.
Go on.