Find the inverse function of f informally.
$f ( x ) = x ^ { 3 }$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x }$
B) $f ^ { - 1 } ( x ) = 2 ( \sqrt [ 3 ] { x } )$
C) $f ^ { - 1 } ( x ) = 3 \sqrt { x }$
D) $f ^ { - 1 } ( x ) = ( \sqrt [ 3 ] { x } ) ^ { 3 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x }$

Question

Find the inverse function of f informally. 
$f ( x ) = x ^ { 3 }$
A) $f ^ { - 1 } ( x ) = - \sqrt [ 3 ] { x }$
B) $f ^ { - 1 } ( x ) = 2 ( \sqrt [ 3 ] { x } )$
C) $f ^ { - 1 } ( x ) = 3 \sqrt { x }$
D) $f ^ { - 1 } ( x ) = ( \sqrt [ 3 ] { x } ) ^ { 3 }$
E) $f ^ { - 1 } ( x ) = \sqrt [ 3 ] { x }$

Quizplus · Accepted Answer

To find the inverse function of f, we want to solve for x in terms of y. So, we start with y = x^3 and solve for x. Taking the cube root of both sides, we get x = y^(1/3). Therefore, the inverse function of f is f^(-1)(x) = y^(1/3) = sqrt[3]{x}. Option E is the only answer choice that matches this.

Find the Inverse Function of F Informally f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3

Find the Inverse Function of F Informally $f ( x ) = x ^ { 3 }$