Question

What is the inverse of f(x)=x+4−−−−√3
?(1 point)
Responses

f−1(x)=x3−4
f inverse left parenthesis x right parenthesis equals x cubed minus 4

f−1(x)=(x−4)3
f inverse left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis cubed

f−1(x)=(x+4)3
f inverse left parenthesis x right parenthesis equals left parenthesis x plus 4 right parenthesis cubed

f−1(x)=x3+4

Answer 1

To find the inverse of the function \( f(x) = \sqrt[3]{x + 4} \), we can follow these steps:

1. Replace \( f(x) \) with \( y \):
\[
y = \sqrt[3]{x + 4}
\]

2. Swap \( x \) and \( y \):
\[
x = \sqrt[3]{y + 4}
\]

3. Solve for \( y \):
- First, cube both sides to eliminate the cube root:
\[
x^3 = y + 4
\]
- Then, isolate \( y \):
\[
y = x^3 - 4
\]

4. Therefore, the inverse function is:
\[
f^{-1}(x) = x^3 - 4
\]

Among the given responses, the correct one is:
\[
f^{-1}(x) = x^3 - 4
\]