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The function f is defined as f(x)=sqrt(4-x). What is the x-coordinate of the point on the function's graph that is closest to the origin?

The function f f is defined as f(x)=4−x f(x)=\sqrt{4-x} .\newlineWhat is the x x -coordinate of the point on the function's graph that is closest to the origin?

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Full solution

Q. The function f f is defined as f(x)=4−x f(x)=\sqrt{4-x} .\newlineWhat is the x x -coordinate of the point on the function's graph that is closest to the origin?
  1. Define Distance Formula: To find the point closest to the origin, we need to minimize the distance from the point (x,f(x))(x, f(x)) to the origin (0,0)(0,0). The distance formula is d=(x−0)2+(f(x)−0)2d = \sqrt{(x - 0)^2 + (f(x) - 0)^2}.
  2. Substitute f(x)f(x): Substitute f(x)f(x) with 4−x\sqrt{4 - x} into the distance formula: d=x2+(4−x)2d = \sqrt{x^2 + (\sqrt{4 - x})^2}.
  3. Simplify Formula: Simplify the distance formula: d=x2+4−xd = \sqrt{x^2 + 4 - x}.

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