Find the Inverse of the function:
f(x)= (x/6)^3 - 7
My answer was f^-1(x) = 6(x+7)^3 is this correct?

Question

Find the Inverse of the function:
f(x)= (x/6)^3 - 7
My answer was f^-1(x) = 6(x+7)^3 is this correct?

anonymous · Answer

You exponent is incorrect.

anonymous · Answer

so would i write it like this? f^-1(x) = [6(x+7)]3

anonymous · Answer

ohhh or is it f^-1(x) = 6(x^3 + 7)?

anonymous · Answer

No, what you did wrong was to assume that 

$$(y/6)^3 =x+7 \to y/6=(x+7)^3$$
That's not how you get rid of exponents. 
if 
$$y^4=x\to y=x^{1/4}$$

anonymous · Answer

okay, so it should be f-1(x) = 18(x + 7) then? Thats the only other answer i got...

anonymous · Answer

You first answer was correct EXCEPT the actual number you put in the exponent. 

if you had $$y=(x/2)^3-1$$
then to find the inverse swap x and y and solve
$$x=(y/2)^3-1$$
then 
$$x+1=(y/2)^3$$
this is where you did something weird. Where  I would take the 1/3 root of both sides: 
$$(x+2)^{1/3} = ((y/2)^3)^{\frac{1}{3}}=y$$
you took both sides to the third power.

anonymous · Answer

Oh okay, i see what i types wrong...thank you so much!

anonymous · Answer

Good luck!