Question

state the domain and range f(x)=x 1/3

Answer 1

is this written as

\[f(x) = 1/3x?\]

Answer 2

oh....its

\[f(x) = x ^{1/3}\]
?

Answer 3

yes

Answer 4

okay....so...are there ANY values of x...that can make this function not = a real number?

Answer 5

keep in mind...raising to the 1/3 power...is the same as taking the cubed root of a number.....so think....are there any numbers you cannot take a cubed root (or a square root) of?

Answer 6

yes 3

Answer 7

....well you can still evaulate 3 correct? it will be a decimal...but still a number right?

let me ask you...what is the square root of -1?

Answer 8

you can't do it

Answer 9

exactly....so that wouldn't be in the domain....what about the square root of 0? can you do it?

Answer 10

nope 0

Answer 11

well yes you can...it would be 0 like you said....as long as you can GET a number...then it exists in the domain...so ...what we have here is...the domain cannot be negative...but can be 0....and can go as high as it wants right? so domain [0,infinity)

range...is the y values.....how big and how small of numbers do you get for plugging in the smallest x you can...and the biggest x you can?

Answer 12

you can do 1 and 3 for the rang right

Answer 13

so say you plug in 0 for x...what does y =?
say you plug in a REALLLLLY big number for x? an even bigger number? is there any limit? no

so that is [0,infinity as well)