1. Tardigrade
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  3. Mathematics
  4. Let the function f(x) =x2 +x + sin x- cos x + log(1 + | x |). be defined over the interval [0, 1]. The odd extension of f(x) to the interval [- 1, 1] is

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Q. Let the function $f(x) =x^2 +x + \sin x-\cos x + \log(1 + | x |).$ be defined over the interval [0, 1]. The odd extension of $f(x)$ to the interval [- 1, 1] is

Relations and Functions

Solution:

Let the function in (a), (b), (c) be denoted by $f_a,f_b,f_c$
Then $ f_a(-x) \neq - f(x) ;f_b (-x)=-f(x);$
$f_c(-x) \neq -f(x) \therefore f_b$ is odd in $(-1,0)$
Hence $f_b$ is odd extension of $f(x)$ in $[-1, 1]$.