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Which of the following functiors are even/ odd, and which are neither even no ogd? (i) \( f ( x ) = \frac { x ^ { 2 } + 1 } { \left( x ^ { 4 } + 1 \right) ^ { 2 } } \) (ini) \( f ( x ) = \log \frac { 1 + x } { 1 - x } \) (ii) \( f ( x ) = x ^ { 2 } + \sec x \) \( ( \) iv \( ) f ( x ) = \left\{ \begin{array} { l } { 0 } \\ { 1 } \end{array} \right. \) if \( x \) is rational if \( x \) irrational

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Similar Questions
Q1
Which of the following functions even and which are odd?
(i) f(x)=x2+7
(ii) f(x)=x+2
(ii) f(x)=x7+2x5
(iv) f(x)=|x|+4
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Q2

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = x2|x| (b) f(x) = ex+e−x

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(e) f(x) = log(x + √x2+1 (f) ax−a−x

(g) f(x) = sinx+cosx (h) sinx×(ex−e−x)


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Q3

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = x2|x| (b) f(x) = ex+e−x

(c) f(x) = log[1−x1+x] (d) log(√x2+1- x)

(e) f(x) = log(x + √x2+1 (f) ax−a−x

(g) f(x) = sinx+cosx (h) sinx×(ex−e−x)


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Q4
If f(x) is an odd function then-
(i)f(−x)+f(x)2 is an even function
(ii)[∣f(x)∣+1] is even where [.] denotes greatest integer function.
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Which of these statements are correct
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Q5
Which of the following functions are even and which are odd?

1) f(x)=x2+7
2) f(x)=x+2
3) f(x)=x7+2x5
4) f(x)=|x|+4
View Solution