Question

Find the inverse of the given function. f(x)= (x+3)^3 -1

Answer 1

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

Explanation:

Step 1: Replace f(x) with y.

`y = (x + 3)^3 - 1`

Step 2: Swap the variables x and y.

`x = (y + 3)^3 - 1`

Step 3: Solve the equation for y.

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

`\sqrt[3]{x+1}=y+3`

`\sqrt[3]{x+1-3}=y`

Step 4: Replace y with
`f^(-1)(x)` to express the inverse function.

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

Answer 2

`y=\sqrt[3]{x+1} -3`

Explanation:

y=(x+3)³-1

to find the inverse, swap the places of the x and y and solve for y

x=(y+3)³-1

y=∛(x+1)-3