Question

Which of the following is an even function?

o f(x) = (x - 1)^2
o f(x) = 8x
O f(x) = x^2- X
O f(x) = 7

Answer 1

An even function is:

f(x) = 7

Explanation:

An even function accomplish the following condition:

f(x)=f(-x) (1)

Applying (1), we have:

• f(x)= (x-1)^2
  `\\eq` f(-x)
  `\\eq` (-x-1)^2
• f(x)= 8x
  `\\eq` f(-x)
  `\\eq` -8x
• f(x)= x^2 -x
  `\\eq` f(-x)
  `\\eq` (-x)^2 +x

• f(x)=7 = f(-x)= 7

The last one is even.