Use the theorem on inverse functions to determine whether f and g are inverse functions of each other. $f ( x ) = 6 x - 1 ; g ( x ) = \frac { x + 1 } { 6 }$
A) f and g are not inverse functions of each other.
B) f and g are inverse functions of each other.

Question

Quizplus · Accepted Answer

To verify if f and g are inverse functions, we need to check if $ f(g(x)) = x $ and $ g(f(x)) = x $. For $ f(g(x)) = 6(\frac{x+1}{6}) - 1 = x $ and for $ g(f(x)) = \frac{6x-1+1}{6} = x $. Both conditions are satisfied, so f and g are inverse functions of each other.

Use the Theorem on Inverse Functions to Determine Whether F f(x)=6x−1;g(x)=x+16f ( x ) = 6 x - 1 ; g ( x ) = \frac { x + 1 } { 6 }f(x)=6x−1;g(x)=6x+1​

Use the Theorem on Inverse Functions to Determine Whether F $f ( x ) = 6 x - 1 ; g ( x ) = \frac { x + 1 } { 6 }$