Question 230619
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(3,(h(x)-3)/2)}}} = x


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


{{{root(3,(x-3)/2)}}} = g(x)


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


You can make g(x) = {{{h^(-1)(x)}}} and your equation becomes:


{{{h^(-1)(x) = root(3,(x-3)/2)}}}


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.