SOLUTION: I need to know if there is a difference between x^3 and cubed root, I did a inverse function problem H(x)=2x^3+3 My answer was y=(x-3)^3/2=h^-1(x)-the answer given was h^-1(x)=cub

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Question 230619: I need to know if there is a difference between x^3 and cubed root, I did a
inverse function problem H(x)=2x^3+3 My answer was y=(x-3)^3/2=h^-1(x)-the answer given was h^-1(x)=cubed root of (x-3)/2 Is this the same?
Answer by Theo(2978) About Me  (Show Source):
You can put this solution on YOUR website!
They are definitely not the same thing.

Your answer is incorrect.

Only thing we need to do is find out why.

The equation was h(x) = 2x^3 + 3.

We will let g(x) represent the inverse function of h(x).

In order to find the inverse function, solve for x and then replace x with g(x) and replace h(x) with x.

Let's do that and see how it works out.

Original equation is h(x) = 2x^3 + 3

Subtract 3 from both sides of the equation to get:

h(x) - 3 = 2x^3

Divide both sides of the equation by 2 to get:

(h(x) - 3)/2 = x^3

take the cube root of both sides of the equation to get:

root%283%2C%28h%28x%29-3%29%2F2%29 = x

Replace x with g(x) and replace h(x) with x to get:

root%283%2C%28x-3%29%2F2%29 = g(x)

g(x) is the inverse function of h(x) and agrees with your book.

You can make g(x) = h%5E%28-1%29%28x%29 and your equation becomes:

h%5E%28-1%29%28x%29+=+root%283%2C%28x-3%29%2F2%29

I'm not sure how you got the answer you got.

Try it again and see if it make more sense.

If you have any questions, send me an email.