Provide an appropriate response.
-Find the inverse of the function $f ( x ) = x + 5$. How is the graph of $f ^ { - 1 }$ related to the graph of $f$ ?
A) $f ( x ) = \frac { 1 } { x } + 5$. The graph of $f ^ { - 1 }$ is a curve intersecting the graph of $f$ at two points equidistant from the $y$-axis.
B) $f ( x ) = x + \frac { 1 } { 5 }$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on the same side of the line $y = x$.
C) $f ( x ) = - x - 5$. The graph of $f ^ { - 1 }$ is a line perpendicular to the graph of $f$ at $x = 5$.
D) $f ( x ) = x - 5$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on opposite sides of the line $y = x$ and are equidistant from that line.

Question

Quizplus · Accepted Answer

To find the inverse of the function, we replace $f(x)$ with $y$, interchange the positions of $x$ and $y$, and solve for $y$:
$$y = x + 5 \Rightarrow x = y + 5 \Rightarrow y = x - 5$$
Thus, the inverse function is $f^{-1}(x) = x - 5$. The graph of the inverse function is a line parallel to the graph of $f$ and they are equidistant from the line $y=x$. Therefore, the best choice is D.

Provide an Appropriate Response f(x)=x+5f ( x ) = x + 5f(x)=x+5

Provide an Appropriate Response $f ( x ) = x + 5$