Question

1)Determine algebraically whether the function is even, odd, or neither even nor odd.
f(x)= x+12/x


2)Find the inverse of the function.

f(x) = 5x^3 - 3

Answer 1

@jim_thompson5910

Answer 2

hint for #1

a function is even if f(-x) = f(x) for all x in the domain of f(x)

a function is odd if f(-x) = -f(x) for all x in the domain of f(x)

Answer 3

odd right?

Answer 4

first off, is f(x)

\[\Large f(x) = x+\frac{12}{x}\]

or is it

\[\Large f(x) = \frac{x+12}{x}\]

Answer 5

ohh I thought it was odd if all the exponents were odd

Answer 6

2nd one

Answer 7

if

\[\Large f(x) = \frac{x+12}{x}\]

then f(-x) = ???

Answer 8

sorry, first one

Answer 9

so it's \[\Large f(x) = x+\frac{12}{x}\]

Answer 10

right?

Answer 11

yes

Answer 12

if \[\Large f(x) = x+\frac{12}{x}\] then f(-x) = ???

Answer 13

f(x)

Answer 14

so even

Answer 15

tell me what the right side is for f(-x)

Answer 16

\[\Large f(x) = x+\frac{12}{x}\]

\[\Large f(-x) = (-x)+\frac{12}{-x}\]

\[\Large f(-x) = ???\]

Answer 17

negatives cancel out, so it would be even

Answer 18

how are they cancelling?

Answer 19

F(-x)=-x?

Answer 20

how would you simplify \[\Large f(-x) = (-x)+\frac{12}{-x}\]

Answer 21

Isnt it already simplified? Im confused

Answer 22

not quite

Answer 23

12/(-x) would turn into -12/x

Answer 24

ohhh

Answer 25

so we get

\[\Large f(x) = x+\frac{12}{x}\]
\[\Large f(-x) = (-x)+\frac{12}{-x}\]
\[\Large f(-x) = -x-\frac{12}{x}\]

Answer 26

So it's clear that f(x) = f(-x) is false

Answer 27

ohhh I understand now, so its even

Answer 28

however, we can factor out a negative 1 which leads us to

\[\Large f(x) = x+\frac{12}{x}\]
\[\Large f(-x) = (-x)+\frac{12}{-x}\]
\[\Large f(-x) = -x-\frac{12}{x}\]
\[\Large f(-x) = -\left(x+\frac{12}{x}\right)\]
\[\Large f(-x) = -f(x)\]

Answer 29

go back to my definitions I posted above

Answer 30

By your definition, it's false, correct?

Answer 31

odd*

Answer 32

what's false?

Answer 33

Ohh I didnt know I could factor out the one

Answer 34

I meant it is odd

Answer 35

it is odd and hopefully you see how

Answer 36

yes i got it, thank you so much

Answer 37

yw