Question

Fine the inverse of g(x)=-2x^+3

Answer 1

`G(y) = (-(y)/(2))^{(1)/(3) }`

Explanation:

We have to find the inverse of the function g(x) where
`y = g(x) = -2x^(3)`.

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
`y = g(x) = -2x^(3)`

⇒
`x^(3)= -(y)/(2)`

⇒
`x = (-(y)/(2))^{(1)/(3) }`

So,
`x = G(y) = (-(y)/(2))^{(1)/(3) }` (Answer)