Exercise 2 | Wiskunde op Tilburg University

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.

Antwoord 2 feedback

Wrong: What happens if

$y=0$ ?

Try again.

Antwoord 3 feedback

Wrong: Consider the minus-sign.

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.