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

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

1 Answer

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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.

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