Question

Which of the following statements is/are true about an even function f(x)?

• A. f(x) = f(-x)
• B. Its graph is symmetrical about origin
• C. f(x) = -f(-x)
• D. Its graph is symmetrical about y-axis

Answer 1

Answer: (A), (D)

Its graph is symmetrical about y-axis

A function f(x) is said to be even if f(x) = f(-x). It means, the value of the function at x = 1 will be same as x = -1. If we plot the function for positive values of x, then we can plot the values of function for negative x. From this, we can say that the function will be symmetrical about y-axis. y = $x^2$ is an example of even function.

To check if a function is even, replace x with -x in the function and check if you get f(x)

For f(x) = $x^2$ , f(-x) = $(-x{)}^2$ = $x^2$ = f(x)

$\Rightarrow$ Its an even function.