Question

I'm not sure how to figure this out. Please help. Show work if you can, please and thank you.

Answer 1

Explanation:

lets start by swapping the x and y variable for f(x)

x=cuberoot(y+1)

x^3=y+1 (you have to raise each side to the power of 3 in order to eliminate the cube root)

y=x^3-1

now lets do the same for g(x) and see if they match (they will)

x=y^3-1

x+1=y^3

cuberoot(x+1)=y

yes they are inverses.

Answer 2

yes

Explanation:

Let us find the inverse of g(x)

To find the inverse, exchange x and y and then solve for x

y = x^3 -1

Exchange x and y

x = y^3 -1

Solve for y

Add 1 to each side

x+1 = y^3-1+1

x+1 = y^3

Take the cube root of each side

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

The two functions are inverses of each other