Question

Need help with this question The answer choices are A-(0,-2)B (1,-1)C (2,0)D(3,3)

Answer 1

Given:

The point (1,-1) lies on the given f(x).

Required:

We need to find the intersection of the inverse function.

Step-by-step explanation:

The parent of the given function is

`y=x^3`

The point (0,0) is moving to (1,-1)

`(x,y)=(0+1,0-1)`

The translation is 1 unit down and 1 unit right side.

The equation of the given graph is

`y=(x-1)^3-1`
`Replace\text{ }x=f^(-1)(y).`
`y=(f^(-1)(y)-1)^3-1`
`y+1=(f^(-1)(y)-1)^3-1+1`
`y+1=(f^(-1)(y)-1)^3`
`\sqrt[3]{y+1}=f^(-1)(y)-1`
`\sqrt[3]{y+1}+1=f^(-1)(y)`
`f^(-1)(x)=\sqrt[3]{x+1}+1`

The graph of the function f(x) and the inverse function:

Final answer:

The intersection point is (2.5, 2.5).