Answer:
[tex]G(y) = (-\frac{y}{2})^{\frac{1}{3} }[/tex]
Step-by-step explanation:
We have to find the inverse of the function g(x) where [tex]y = g(x) = -2x^{3}[/tex].
If we have a function y = f(x), then expressing the value of x in terms of y i.e. x = F(y) is called the inverse of the function y = f(x).
So, inverse of y = f(x) is x = F(y).{Where f and F are two different functions}
Now, we have [tex]y = g(x) = -2x^{3}[/tex]
⇒ [tex]x^{3}= -\frac{y}{2}[/tex]
⇒ [tex]x = (-\frac{y}{2})^{\frac{1}{3} }[/tex]
So, [tex]x = G(y) = (-\frac{y}{2})^{\frac{1}{3} }[/tex] (Answer)
