Find the inverse function informally $f ( x ) = 2 x$ . Verify that $f \left( f ^ { - 1 } ( x ) \right) = x$ and $f ^ { - 1 } ( f ( x ) ) = x$
A) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ , $f \left( f ^ { - 1 } ( x ) \right) = x ^ { - 1 }$ , $f ^ { - 1 } ( f ( x ) ) = x$
B) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ , $f \left( f ^ { - 1 } ( x ) \right) = 2 x$ , $f ^ { - 1 } ( f ( x ) ) = 3 x$
C) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ , $f \left( f ^ { - 1 } ( x ) \right) = x$ , $f ^ { - 1 } ( f ( x ) ) = 2 x$
D) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ , $f \left( f ^ { - 1 } ( x ) \right) = 3 x$ , $f ^ { - 1 } ( f ( x ) ) = x$
E) $f ^ { - 1 } ( x ) = \frac { x } { 2 }$ , $f \left( f ^ { - 1 } ( x ) \right) = x$ , $f ^ { - 1 } ( f ( x ) ) = x$

Question

Quizplus · Accepted Answer

The inverse function of $f(x) = 2x$ is $f^{-1}(x) = \frac{x}{2}$ because applying $f$ to $f^{-1}(x)$ or vice versa returns the original input $x$, satisfying the conditions for inverse functions.

Find the Inverse Function Informally f(x)=2xf ( x ) = 2 xf(x)=2x

Find the Inverse Function Informally $f ( x ) = 2 x$