Question

In Parity of function:

if f(x) odd and g(x)=f(x)+2 Then g(x) is:?
(a) Even
(b) odd
(c) neither odd nor Even ​

Answer 1

(c) neither odd nor Even

Explanation: ​

f(x) odd ⇒ f(-x) = - f(x)

⇒ g(-x) = f(-x) + 2 = - f(x) + 2

Since - f(x) + 2 ≠ - f(x) - 2 and - f(x) + 2 ≠ f(x) + 2

Then g(-x) ≠ - g(x) and g(-x) ≠ g(x)

Then g is neither odd nor even