show that f(x)=(x-2)^3+8 is one to one algebraically

Question

Allison · Answer

Was the other one I answered right?

kaylak · Answer

idk im trying to finish an assignment please get me some help here

Allison · Answer

Okay hold on.

kaylak · Answer

ok?

Ultrilliam · Answer

@Nnesha @sillybilly123 @Vocaloid @layla @Hero

Don't mind me, just tagging our math helpers so they see this when they are on

Allison · Answer

One to one means every x corresponds to one y, the only way I know how to do that is by evaluating every single value of x which is impossible so I don't know how to answer this question. :/

Nnesha · Answer

If the function pass the horizontal line test then the function is 1 to 1. Like she said ^ 
if  two different inputs give you the same outputs then the function is not 1 to 1.  Algebraically you have to show that if $$f(a)=f(b)  ~~~ ~~then~~a=b$$ 
if a=b then the function is 1 to 1

Nnesha · Answer

replace x with a
replace x with b
$$\large\rm f(\color{red}{a})=f(\color{blue}{b})$$$$\large\rm (\color{red}{a}-2)^3+8=(\color{blue}{b}-2)^3+8$$
solve the equation for a or for b
first subtract 8 both sides 
$$\large\rm f(\color{red}{a})=f(\color{blue}{b})$$$$\large\rm (\color{red}{a}-2)^3=(\color{blue}{b}-2)^3$$
now you can take cube root both sides and simplify

Allison · Answer

Yes! @Nnesha sorry about that, but thank you c:

Nnesha · Answer

sorry for nothing?

Allison · Answer

No I meant sorry for like, not knowing how to do it x.x

Nnesha · Answer

`if  two different inputs give you the same outputs then the function is not 1 to 1.  Algebraically you have to show that if ` 
correction 
if  two different inputs give you the same outputs then the function `is `1 to 1.  Algebraically you have to show that if

Nnesha · Answer

ohh i see. no need to say sorry especially for not knowing how to solve a question which  u haven't  learnd it yet

Allison · Answer

Thank you~ :*