Select the correct statement from the following.
A) $f ( x ) = \frac { 5 } { 5 x - 1 } \text { for } x \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { 5 x } \text { for } x 0 \text { are inverses of each other }$ .
B) $f ( x ) = \frac { 1 } { 5 x - 1 } \text { for } x \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { 5 x } \text { for } x 0 \text { are inverses of each other }$ .
C) $f ( x ) = \frac { 5 } { 5 x - 1 } \text { for } x \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { x } \text { for } x 0 \text { are inverses of each other }$ .

Question

Select the correct statement from the following.
A) $f ( x ) = \frac { 5 } { 5 x - 1 } \text { for } x > \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { 5 x } \text { for } x > 0 \text { are inverses of each other }$ .
B) $f ( x ) = \frac { 1 } { 5 x - 1 } \text { for } x > \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { 5 x } \text { for } x > 0 \text { are inverses of each other }$ .
C) $f ( x ) = \frac { 5 } { 5 x - 1 } \text { for } x > \frac { 1 } { 5 } \text { and } g ( x ) = \frac { x + 5 } { x } \text { for } x > 0 \text { are inverses of each other }$ .

Quizplus · Accepted Answer

We need to check if the composition of the two functions gives us the identity function. 
Let's first find $f(g(x))$: 
$$f(g(x))=f\left(\frac{x+5}{5x}\right)=\frac{5}{5\left(\frac{x+5}{5x}\right)-1}=\frac{5x}{x+5}=g(f(x))$$
So, $f$ and $g$ are indeed inverses of each other. Option A is the only one that represents the correct functions.

Select the Correct Statement from the Following B) C)

Select the Correct Statement from the Following
B)
C)