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Graphs of two functions are shown. What is the value of f(2) + g(2)?

Mathematics

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Answer

You've made a good start on the graph, sthamntungwa! The general shape and reflection across the y=xy=x line are visible.

Here's some feedback to make it perfect:

  1. Axis Labels and Scale: Ensure your x and y axes are consistently numbered at regular intervals (e.g., 1, 2, 3, ... for each major grid line). This makes it easier to read specific points.
  2. Endpoints: Clearly mark the endpoints of each line segment with either an open circle (for points not included, like (0,−5)(0,-5) for f(x)f(x) and (−5,0)(-5,0) for f−1(x)f^{-1}(x)) or a closed circle (for points included, like (6,7)(6,7) for f(x)f(x) and (7,6)(7,6) for f−1(x)f^{-1}(x)).
  3. Line Labels: Label each line directly on the graph: f(x)f(x), f−1(x)f^{-1}(x), and y=xy=x.
  4. Point on y=xy=x: You've drawn y=xy=x correctly through the origin. You can also explicitly mark another point on it, like (1,1)(1,1), as requested in the original question.

The lines themselves appear to be in the correct positions relative to each other and the line y=xy=x. Just refine the details for full marks!

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