Question

Which functions are even? Check all of the boxes that apply.

Answer 1

Answer:

Please check the explanation.

Step-by-step explanation:

We know that:

A function is even if f(-x)=f(x) for all x ∈ R

A function is odd if f(-x)=-f(x) for all x ∈ R

1)

f(x)=x-x

f(-x)=-x-(-x)=-x+x=0

Parity of 0:  Even and odd

2)

f(x) = x² – 3x + 2

f(-x)=(-x)²-3(-x)+2

     = x²+3x+2

As

f(-x) ≠ f(x) and also f(-x) ≠ -f(x)

So, f(x) = x² – 3x + 2 is neither od nor even

3)

f(x)=(x-2)

f(-x)=(-x-2)

f(-x) ≠ f(x) and also f(-x) ≠ -f(x)

So, f(x)=(x-2) is neither odd nor even

4)

f(x) = 1x¹

f(-x)=1(-x)¹

      =-x

As

f(-x)=-f(x)

Thus, f(x) = 1x¹ is odd function.