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Question

If in the equation y = f(x), f(x) is even function then

A
f(x)=f(x)
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B
f(x)=f(x)
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C
Its graph is symmetric about y-axis.
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D
If (x, y) is a point on its graph, then (-x, y) is also on the same graph.
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Solution

The correct option is D If (x, y) is a point on its graph, then (-x, y) is also on the same graph.
A function f(x) is said to be even, if it remains unchanged after replacing x in the equation with -x.
i.e., f(x)=f(x)
As both x and -x give the same output from the function. Hence, its graph will be symmetric about y-axis.

There will be two values of x for one value of y, one will be +x and other will be -x. Hence, in the graph if (x, y) is a point, then (-x, y) will also be a point.

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