Question

State the Domain and Range of the function
2x^3-1/5x^3-16
Please show me how yhu worked it out~

Answer 1

Its a rational function, so the denominator cannot equal zero. The domain is the set of real numbers that make the function defined.

Answer 2

So, I would look at the highest exponent right?
That's what I was told... But the highest exponent is 3 and it's on top and bottom.

Answer 3

is it this
\(\dfrac{2x^3-1}{5x^3-16}\)

Answer 4

Yes

Answer 5

\(\large\tt \begin{align} \color{black}{5x^3-16\neq 0
}\end{align}\)

Answer 6

That's... The domain? Or the first step I would take to find it.

Answer 7

that is not the domain ,the solutions which this equation will give will not be part of the domain

Answer 8

http://www.wolframalpha.com/input/?i=x%5E3%3D%5Cfrac%7B16%7D%7B5%7D

Answer 9

here u can exclude the imaginary solutions

Answer 10

Will it show me, like... How it did it? The steps so I know how to solve the other problems like this?

Answer 11

u can solve it by formula
\(\Large a^3-b^3=(a-b)(a^2+ab+b ^2)\)

Answer 12

\(\large\tt \begin{align} \color{black}{5x^3-16=0\\
x^3-\dfrac{16}{5}\\
=x^3-2^3(\dfrac{ 2}{5})^{\frac{3}{3}}
}\end{align}\)

Answer 13

\(\Large a^3-b^3=(a-b)(a^2+ab+b ^2)\)

from this formula

\(\large\tt \begin{align} \color{black}{(a^2+ab+b ^2)
}\end{align}\)
part will give imaginary solutions

so u have to just ignore it

Answer 14

so we are left with
\(\Large\tt \begin{align} \color{black}{(a-b)
}\end{align}\)

Answer 15

r u getting it?

Answer 16

\(\Large\tt \begin{align} \color{black}{(a-b)
\implies x-(2\sqrt[3]{\dfrac{ 2}{5}})=0\\
x=(2\sqrt[3]{\dfrac{ 2}{5}})
}\end{align}\)

Answer 17

domain =
\(\Large\tt \begin{align} \color{black}{x\in \mathbb{R}:x\neq (2\sqrt[3]{\dfrac{ 2}{5}})
}\end{align}\)
where \(\Large \mathbb{R}\)=real numbers

Answer 18

I... Kind of get it...
So then the range is... what the y values can be.
which would be...
\[r(x)\in \mathbb{R},0>x>\infty \] ?

Answer 19

here when
\(\large\tt \begin{align} \color{black}{f(x)=\dfrac{2}{5}\\
\dfrac{2}{5}=\dfrac{2x^3-1}{5x^3-16}\\
10x^3-32=10x^3-5\\}\end{align}\)

Answer 20

\(\large\tt \begin{align} \color{black}{
-32\neq -5\\}\end{align}\)

Answer 21

So how would I write that in terms of range?

Answer 22

\(\large\tt \begin{align} \color{black}{f(x)\in \mathbb{R}:f(x) \neq \dfrac{2}{5}
}\end{align}\)

Answer 23

>.< I was way wrong.
If I do another one and try it, do yhu mind if I tag yhu and yhu can check what I did? I have 2 more kind of like this.

Answer 24

i will try

Answer 25

Thank yhu~ c: