Parent function of g(x)=-(x-1)^3

Question

I need to know the steps that I do in order to solve the equation

Answer 1

Hello, thank you for taking the time to post your question!

You can think of the parent function as being like the simplest form of a family of functions. So it’s what the most basic form of the function looks like before transformations are applied.

For this expression of g(x) = -(x – 1)^3, the starting functional form is the cubic, f(x) = x^3.

So the parent function here is f(x) = x^3

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Jonathan:

 

You say solve the equation.  The only "equation" I see in g(x) = -(x-1)³.  So I will solve it for you.

 

Let g(x) = y. Then

 

y = -(x-1)³.

 

(-y) = (x - 1)³.

 

(-y)^(1/3) = (x - 1)

 

x = 1 + (-y)^(1/3).

 

This equation gives you a value for x, given a value for y.   This equation is actually an "inverse" function.

 

Dattarabhakar (Dr. G.)