Question

Which graph shows f(x) = 1/2 x + 2 and its inverse?

Answer 1

Step-by-step explanation

We have a line given by the following function:

`f(x)=(1)/(2)x+2.`

The inverse function of f(x) is the function g(x), that satisfies:

`g(f(x))=x.`

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:

`\begin{gathered} x=f(y)=(1)/(2)y+2, \\ x-2=(1)/(2)y, \\ y=2*(x-2), \\ y=2x-4. \end{gathered}`

So the inverse function is:

`g(x)=2x-4.`

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.