Question

Identify the errors made in finding the inverse ofy = x2 + 12x.x= y2 + 12xy2 = x - 12xy2=-11xy=-11x, for x > 0Describe the three errors?

Answer 1

First, starting from the equation:

`y=x^2+12x`

We should change every x for a y and every y for an x, so:

`x=y^2+12y`

In the text, the first step was:

`x=\questeq y^2+12x`

So, the first mistake was not to change the linear term 12x for 12y.

Another mistake was made from the following steps:

`\begin{gathered} y^2=-11x \\ y=\sqrt[]{-11x},x\ge0 \end{gathered}`

The expression inside the square root must be greater or equal to 0, then:

`\begin{gathered} -11x\ge0 \\ \Rightarrow x\le0 \end{gathered}`

So, the second mistake was not to identify the domain of x correctly.

A third mistake is that the square root of y^2 is not y, it is |y|. So:

`\begin{gathered} y^2=-11x \\ \Rightarrow|y|=\sqrt[]{-11x} \\ \Rightarrow y=\pm\sqrt[]{-11x} \end{gathered}`