Question

Let $▼$x be defined as $x+\frac{1}{x}$ for all nonzero integers $x$. If $▼$ $x=t$, where $t$ is an integer, which of the following is a possible value of $t$?

• A. $1$
• B. $0$
• C. $-1$
• D. $-2$
• E. $-3$

Answer 1

Answer: (D)

$-2$

We ignore the triangle sign and just look at it as $x+\frac{1}{x}=t$. We need t to equal an integer (a whole number - can be positive or negative)

If we look closely since there is $\frac{1}{x}$

We know that the x needs to be a $1$ or $-1$ (it can't be any number greater because that would be a fraction and it can't be $0$ because $\frac{1}{0}$ doesn't exist.

so just plug in 1 and you get $1+\frac{1}{1}=2$,

However, $2$ is not one of the answers.

Plug in $-1$ and you get $-1+\frac{1}{-1}=-2$ and that would be D.