# Thread: [SOLVED] f(x)=-f(x)

1. ## [SOLVED] f(x)=-f(x)

Barron's SAT Math II. Page 12 #2
A function is said to be even if f(x)=-f(x). Which of the following is NOT an even function

a) y= lxl
b)y=secx
c) y=logx^2
d) y=x^2+sinx
e) y=3x^4-2x^2+17

I know a), c) and e) are even functions. But I can't decide between b) and d). What does sec in y=secx mean exactly?

Thanks in advance! (:

2. first of all the definition of even function as you present it is wrong, the only function that satisfies:
$
f(x) = - f(x)$

is 0.

The correct definition is:

$
f(x) = f( - x)$

b)

$
y = \sec (x) = \frac{1}
{{\cos (x)}}$

and we already know that cos(x) is an even function, thus b is even.

d)

$
\begin{gathered}
y(x) = x^2 + \sin (x) \hfill \\
y( - x) = x^2 - \sin (x) \hfill \\
\end{gathered}$

so obviously d is not an even function.