The diagram shows the distance between an object and a lens and the distance between the lens and the image it creates of the object. and represent the focal points of the two-sided lens. (Note that these points are symmetric about the lens at line .) Use the diagram and the function to find and if the focal length of the lens is and .

Define the variables in the function.

Substitute the defined variables into the given function and simplify.

Graph the simplified equation.

Describe the domain of the function and what that implies for the number of possible solutions for and .

Solve to find the value(s) of as described in step 4.

Find and interpret the solutions in terms of the locations of the object and image in relation to the lens.

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