Find the inverse of the function.
f(x)=3squareroot x/8-4
i keep getting f−1(x)=512x3+6144x2+24576x+32768

- anonymous

- chestercat

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- anonymous

when these are the answer choices f-1(x) = [8(x + 4)]3
f-1(x) = 8(x + 4)3
f-1(x) = 8(x3 + 4)
f-1(x) = 24(x + 4)

- anonymous

Can you draw the function?

- anonymous

Because it's not very clear. :)

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## More answers

- Jack1

hi... is this your function?
\(\Large f(x)=3 \times \sqrt{ \frac x{8-4}}\)

- anonymous

no

- Jack1

is it this?
\(\Large f(x)=3 \times \sqrt{ \frac x8-4}\)

- anonymous

\[f(x)=\sqrt[3]{x/8}-4\]

- anonymous

Step 1: Change f(x) to y.
Step 2: Flip x and y. So y will become x, and x will become y.
Step 3: Make the function look like this--> y=mx+b

- anonymous

|dw:1439341791162:dw|

- anonymous

|dw:1439341863512:dw|

- anonymous

Did you understand it or not?

- anonymous

After that, make the function look like y=mx+b.

- anonymous

so its c?

- anonymous

No.

- anonymous

how

- anonymous

Add 4 on both sides. What will you get?|dw:1439342093820:dw|

- anonymous

i was almost positive it was either c or d but now i am very confused

- anonymous

lol

- anonymous

then can you show me how you did it?

- anonymous

what is funny?

- anonymous

lol because i'm trying to hep you but it seems like you're saying that my answer is already wrong :D

- anonymous

I am not saying that at all I am saying you are right, and i guess i started wrong form the beginning

- anonymous

just a quick question: do you know how to add 4 on both sides?

- anonymous

nope

- anonymous

oh if you don't know, then you can say so. you shouldn't keep people waiting :)

- anonymous

sorry

- anonymous

do you remember this in algebra 1? |dw:1439342702568:dw|

- anonymous

just a quick yes or no is fine

- anonymous

no

- anonymous

Wait we are both in FLVS Pre-Calculus class right? So basically, you just need to add 4 to x, and the 4 in the right side is now removed. |dw:1439342854963:dw|

- anonymous

And then to remove the cube root, you just simply cube it. So from the left side, x+4 will now become \(\huge (x+4)^3\). And the right side will become \(\huge\frac{ y }{ 8 }\).

- anonymous

ohhhhh i see

- anonymous

The function will now look like this. Now to remove the 1/8 in y/8, simply multiply it by its reciprocal--8--on both sides.. |dw:1439343067959:dw|

- anonymous

Multiply 8 on both sides. |dw:1439343171462:dw|

- anonymous

From here, what do you think the answer will be? |dw:1439343201548:dw|

- Jack1

if i could double medal u i would, awesome explanation @mathway

- anonymous

i second Jack! im starting to completely understand!

- anonymous

lol i'm flattered

- anonymous

i have question though, what is the difference between the brackets and the parentheses?

- anonymous

What do you mean? They are just the same, but not totally. I can't explain it.

- anonymous

I was asking you a question btw @Abbs__ :D look at the drawing above

- anonymous

f-1(x)=8(x+4)3

- anonymous

Yes. :)

- anonymous

You rock!

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