Question

Is the function f(x)=1/x even, odd,or neither even or odd? justify your answer?

Answer 1

\[\large\rm \color{orangered}{f(x)=\frac{1}{x}}\]Can you tell what happens when we plug a negative x into the function?\[\large\rm f(-x)=?\]

Answer 2

we get -1

Answer 3

Mmmmm no.
We didn't plug -1 into the function,
we plugged -x in place of x.

Answer 4

i dont know i gues -x

Answer 5

\[\large\rm f(-x)=\frac{1}{(-x)}\]Replacing x with -x gives us this, yes?

Answer 6

The brackets are not necessary I suppose

Answer 7

yes

Answer 8

\[\large\rm f(-x)=-\color{orangered}{\frac{1}{x}}\]Let's pull the negative out front,
and recognize that this 1/x is the f(x) function that we started with,\[\large\rm f(-x)=-\color{orangered}{f(x)}\]

Answer 9

Odd functions have this property, f(-x) = -f(x).
So we've shown that the function is `odd`.