1. Tardigrade
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  4. Let f(x) be an odd function defined on (-∞, ∞) and g(x) be an even function defined on (-∞, ∞).If f(x)-g(x)=x2+5 x+7, then g(2) is equal to

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Q. Let $f(x)$ be an odd function defined on $(-\infty, \infty)$ and $g(x)$ be an even function defined on $(-\infty, \infty)$.If $f(x)-g(x)=x^2+5 x+7$, then $g(2)$ is equal to

Relations and Functions - Part 2

Solution:

We have $f(x)-g(x)=x^2+5 x+7$....(1)
Replace $x \rightarrow-x$ in equation (1), we get
$f (- x )- g (- x )= x ^2-5 x +7 $
$\Rightarrow - f ( x )- g ( x )= x ^2-5 x +7 $
$\Rightarrow f ( x )+ g ( x )=- x ^2+5 x -7$....(2)
$\therefore $ On solving (1) and (2),
we get $f ( x )=5 x$ and $g ( x )=- x ^2-7$
Hence $g(2)=-11$