If f(−x) = f(x) for all x, then the function f(x) is symmetric with respect to the y−axis.TrueFalse

The statement is true.

Explanation

If $f(-x) = f(x)$ for all $x$, this means that the function takes the same value at $x$ and at $-x$. This property of the function indicates that it is symmetric with respect to the y-axis.

In more formal terms:

• A function $f(x)$ is defined to be even if it satisfies the condition $f(-x) = f(x)$ for every $x$ in its domain.
• The symmetry with respect to the y-axis means that the function looks the same on both sides of the y-axis.

Thus, because the condition $f(-x) = f(x)$ holds for all $x$, the conclusion that the function is symmetric with respect to the y-axis is correct.

Final Answer

True