Question

Let f(x) = 2 + 1/x. Which of the following are zeros of f(x)?
*check all that apply*
a. x = 0
b. x = -1/2
c. x = 1/2
d. none of the above

Answer 1

You need to find x, by setting f(x) equal to zero, like so \[\Large 2 + \frac{ 1 }{ x } = 0\]
Try solving that for x.

Answer 2

is it -2?

Answer 3

No... but start by subtracting 2 from both sides.

Answer 4

If you use x=-2,

2+(1/-2) = 3/2, which is not zero.

Answer 5

So when I subtract 2 from both sides I get 1/x = -2

Answer 6

Correct. Now, you can cross-multiply and then find x. Write the -2 like so:

\[\Large \frac{ 1 }{ x} = \frac{ -2 }{ 1}\]

or you can just invert both fractions to find x.

Answer 7

When I cross multiply should I get 1 = -2x?

Answer 8

Or x = -2?

Answer 9

1 = -2x is correct. x=-2 is not.

Answer 10

Thought so. So what do I do next?

Answer 11

Divide?

Answer 12

Yes.

Answer 13

1/-2? Or -1/2?

Answer 14

So is it just b?

Answer 15

1/-2? Or -1/2

those are the same thing

\[\Large \frac{ -1 }{ 2 } = \frac{ 1 }{ -2 } = -\frac{ 1 }{ 2 }\]