Given the function f(x)=x3−3

Question

, create its inverse.(1 point)
Responses

f−1(x)=x−3−−−−−√3
f inverse left parenthesis x right parenthesis equals root index 3 Start Root x minus 3 End Root

f−1(x)=x+3−−−−−√3
f inverse left parenthesis x right parenthesis equals root index 3 Start Root x plus 3 End Root

f−1(x)=x−−√3+3
f inverse left parenthesis x right parenthesis equals root index 3 Start Root x End Root plus 3

f−1(x)=x3+3−−−−−√3

Answer 1

To find the inverse of the function \( f(x) = x^3 - 3 \), we need to follow these steps:

1. Replace \( f(x) \) with \( y \): \[ y = x^3 - 3 \]

2. Solve for \( x \) in terms of \( y \): \[ y + 3 = x^3 \] \[ x = (y + 3)^{1/3} \]

3. Replace \( y \) with \( x \) to write the inverse function: \[ f^{-1}(x) = (x + 3)^{1/3} \]

Among the given responses, the correct form of the inverse function is: \[ f^{-1}(x) = \sqrt[3]{x + 3} \]

So, the correct answer is: f^{-1}(x) = \sqrt[3]{x + 3}.