Explanation
We have a line given by the following function:
[tex]f(x)=\frac{1}{2}x+2.[/tex]
The inverse function of f(x) is the function g(x), that satisfies:
[tex]g(f(x))=x.[/tex]
To find the inverse function, we replace x by y in the equation of f(x), and then we equal to x and solve for y, we get:
[tex]\begin{gathered} x=f(y)=\frac{1}{2}y+2, \\ x-2=\frac{1}{2}y, \\ y=2*(x-2), \\ y=2x-4. \end{gathered}[/tex]
So the inverse function is:
[tex]g(x)=2x-4.[/tex]
Plotting f(x) and g(x), we get the following graph:
Comparing this graph with the options, we conclude that option A is the correct answer.
Answer
Graph A.
