Determine whether the following functions are even or odd or neither even nor odd :
(i) sin (x 2 + 1) (ii) x + x 2
(iii) f(x) = x 
(iv) f(x) = sin x + cos x
(v) f(x) = (x 2 – 1) | x |
(vi)f(x) = 
, where [.] is GIF.
Text Solution
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(i) even,
(ii) neither even nor odd
(iii) even,
(iv) neither even nor odd(v) even
(vi) even
Sol. (i) f(x) = sin (x 2 +1) ⇒ f(– x) = f (x) = even function
(ii) f(x) = x + x 2 ⇒ f(– x) = x 2 – x ≠ f (x) or – f(x) Neither even nor odd function
(iii) f(x) = x 
⇒ f(–x) = – x 
⇒ f(–x) = x 
= f(x) even function
(iv) f(x) = sin x + cos x ⇒ f(– x) = – sin x + cos x ≠ f(x) or – f(x)
Neither even nor odd.
(v) f(x) = (x 2 – 1) |x| ⇒ f(–x) = f(x) even function.
(vi) f(x) = 
⇒ f(x) = 
f(x) = 
b f(x) = f(–x)
even function
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