Question

12.Which of the following is an even function?
A) f(x) = 3 cos x + 4
B) f(x) = 2 sin x + 3
C) f(x) = 2x + x
D) 2 sin x + 3 cos x​

Answer 1

Answer:

( A) f(x) = 3cosx+4

Step-by-step explanation:

Condition for even function is as following

f(x) = f(-x)

Now,

in option

( A) f(x) = 3cosx+4

f(-x) = 3cos(-x) +4 = 3cosx+4 = f(x)

f(x) = f(-x)

So, f(x) is an even function.

(B) f(x) = 2sinx+3

so, f(-x) = 2sin(-x)+3 = -2sinx+3

f(-x) is not equal to f(x). So, f(x) is not an even function.

C) f(x) = 2x + x

so, f(-x) = 2(-x)+(-x) = -2x - x = -(2x + x) = -f(x)

f(-x) is not equal to f(x). So, f(x) is not an even function

D) f(x) = 2 sin x + 3 cos x

so, f(-x) = 2sin(-x) + 3cos(-x) = -2sinx + 3cosx

f(-x) is not equal to f(x). So, f(x) is not an even function

$\sin( - \alpha ) = - \sin( \alpha ) \\ \cos( - \alpha ) = \cos( \alpha ) \\ \tan( - \alpha ) = - \tan( \alpha )$