Question

f(x)=2x^3 - x^2 + 1/2x
Let g(x)=f(2/3x)
What is g(x) in terms of x? Please help me out I'm reviewing for eoc and would like to know how to do this

Answer 1

@ganeshie8

Answer 2

\(\LARGE f\left(\frac{2}{3}x\right)\) means you replace every x in f(x) with (2/3)x like so...


\[\Large f(x) = 2x^3 - x^2 + \frac{1}{2}x\]

\[\Large f({\color{red}{x}}) = 2{\color{red}{x}}^3 - {\color{red}{x}}^2 + \frac{1}{2}{\color{red}{x}}\]

\[\Large f\left({\color{red}{{\frac{2}{3}x}}}\right) = 2\left({\color{red}{{\frac{2}{3}x}}}\right)^3 - \left({\color{red}{{\frac{2}{3}x}}}\right)^2 + \frac{1}{2}\left({\color{red}{{\frac{2}{3}x}}}\right)\]

Do you see what to do next?

Answer 3

On 2(2/3x)^3 is where I am having the most problem

Answer 4

when you cube something, you're multiplying it by itself 3 times

examples

8^3 = 8*8*8 = 512
5^3 = 5*5*5 = 125
7^3 = 7*7*7 = 343

make sense?

Answer 5

Yes, So would it be 6/9x then multiplied by 2? Because if i do 2/3 I get decimals that dont necessarily make sense.

Answer 6

so you'll use that same idea for (2/3x)^3

Answer 7

I have the answer sinceI am using one of the eoc reviews but I am confused as to how they got what they did

Answer 8

\[\Large \left(\frac{2}{3}x\right)^3 = \left(\frac{2}{3}x\right)*\left(\frac{2}{3}x\right)*\left(\frac{2}{3}x\right)\]

Answer 9

Oh okay that makes sense now

Answer 10

\[\Large \left(\frac{2}{3}x\right)^3 = \left(\frac{2}{3}x\right)*\left(\frac{2}{3}x\right)*\left(\frac{2}{3}x\right)\]

\[\Large \left(\frac{2}{3}x\right)^3 = \left(\frac{2}{3}*\frac{2}{3}*\frac{2}{3}\right)*(x*x*x)\]

\[\Large \left(\frac{2}{3}x\right)^3 = \frac{2*2*2}{3*3*3}*x^3\]

\[\Large \left(\frac{2}{3}x\right)^3 = \frac{8}{27}x^3\]

Answer 11

Then multiply the 8 by 2?

Answer 12

8 by the 2? what do you mean?

Answer 13

oh I see now, yes

Answer 14

the 2 from 2x^3

Answer 15

since it was originally 2(2/3x)^3

Answer 16

Yes

Answer 17

`Then multiply the 8 by 2?`
yes to get
\[\Large 2*\left(\frac{2}{3}x\right)^3 = 2*\frac{8}{27}*x^3=\frac{2*8}{27}*x^3=\frac{16}{27}x^3\]

Answer 18

Gotcha.

Answer 19

so then for (2/3x) ^2 would you basically just do 2*2 and then 3*3 to get 4/9 and x*x so it would be 4/9x^2

Answer 20

very good

Answer 21

how about the last part with 1/2 times (2/3x)