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Question 193

The graph of the function $$y = f(x)$$ is symmetrical about the line $$x = 2$$, then

Solution

Let a function be symmetrical about a vertical line given by:

$$ x = a $$

Geometrically, this means that if we move a distance of x to the right of the line or a distance of x to the left of the line, the corresponding outputs of the function are identical. This property can be written as:

$$ f(a + x) = f(a - x) $$

The problem states that the graph is symmetrical about the specific line:

$$ x = 2 $$

Substitute the value of $$ a = 2 $$ into the symmetry relation formula:

$$ f(2 + x) = f(2 - x) $$

Final Answer:

The mathematical relation for the symmetry is $$ f(2 + x) = f(2 - x) $$.

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