Find the inverse function of f informally. F(x) = x⁴ A) $f ^ { - 1 } ( x ) = 4 \sqrt { x }$ B) $f ^ { - 1 } ( x ) = \sqrt [ 4 ] { x }$ C) $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt [ 4 ] { x } }$ D) $f ^ { - 1 } ( x ) = ( \sqrt [ 4 ] { x } ) ^ { 4 }$ E) $f ^ { - 1 } ( x ) = - \sqrt [ 4 ] { x }$

Question

Quizplus · Accepted Answer

The given function $f(x) = x^{1/4}$ raises x to the 1/4th power, which means finding the 4th root of x. The inverse function, $f^{-1}(x)$, undoes this operation, meaning it will take the output of the function and raise it to the power that gives back the original input. Therefore, the inverse function is $f^{-1}(x) = \sqrt[4]{x}$, which corresponds to choice B.

Find the Inverse Function of F Informally f−1(x)=4xf ^ { - 1 } ( x ) = 4 \sqrt { x }f−1(x)=4x​

Find the Inverse Function of F Informally $f ^ { - 1 } ( x ) = 4 \sqrt { x }$