Which statement(s)verify that $f ( x ) = 9 x - 1$ and $g ( x ) = \frac { 1 } { 9 } ( x + 1 )$ are inverse?
A) $f ( x ) \cdot g ( x ) = ( 9 x - 1 ) \frac { 1 } { 9 } ( x + 1 ) = - 1$
B) $f ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x , g ( f ( x ) ) = \frac { 1 } { 9 } ( 9 ( x - 1 ) + 1 ) = x$
C) $f ( g ( x ) ) = \left( 9 \left( \frac { 1 } { 9 } x \right) + 1 \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x$
D) $f ( g ( x ) ) = 9 \left( \frac { 1 } { 9 } ( x + 1 ) \right) - 1 = x ; g ( f ( x ) ) = \frac { 1 } { 9 } ( ( 9 x - 1 ) + 1 ) = x$
E) $\frac { f ( x ) } { g ( x ) } = \frac { 9 ( x - 1 ) } { 9 ( x + 1 ) } = - 1$

Question

Quizplus · Accepted Answer

Two functions are inverses if and only if $f(g(x)) = x$ and $g(f(x)) = x$. Choice D correctly applies these operations and simplifies to show that each composition equals $x$, verifying that $f$ and $g$ are inverse functions.

Which Statement(s)verify That f(x)=9x−1f ( x ) = 9 x - 1f(x)=9x−1

Which Statement(s)verify That $f ( x ) = 9 x - 1$