Ed:.06 a function δ(x) is a composite function which is as follow [{(f ○ g)(x)} ○ {(g ○ f)(x)}] ○ [{(f ′ ○ g ′)(x)} ○ {(g ′ ○ f ′)(x)}] where f(x) = Π_(n = 1) ^∞ ((nx^3 − nx^2 − nx −n)/(n^3 x − n^2 x − nx −x)) g(x)= f ′′(x) ∫_( ψ) ^( δ) δ(x) dx ∈ R\Q ? true or false?


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Question Number 216910 by Marzuk last updated on 24/Feb/25
$Ed:.06 a function δ(x) is a composite function which is as follow [{(f ○ g)(x)} ○ {(g ○ f)(x)}] ○ [{(f ′ ○ g ′)(x)} ○ {(g ′ ○ f ′)(x)}] where f(x) = Π_(n = 1) ^∞ ((nx^3 − nx^2 − nx −n)/(n^3 x − n^2 x − nx −x)) g(x)= f ′′(x) ∫_( ψ) ^( δ) δ(x) dx ∈ R\Q ? true or false?$
$E d : . 06$ $a f u n c t i o n δ (x) i s a c o m p o s i t e f u n c t i o n$ $w h i c h i s a s f o l l o w$ $[{(f \circ g) (x)} \circ {(g \circ f) (x)}] \circ [{(f^{'} \circ g^{'}) (x)} \circ {(g^{'} \circ f^{'}) (x)}]$ $w h e r e$ $f (x) = \underset{n = 1}{\prod^{\infty}} \frac{{n x}^{3} - {n x}^{2} - n x - n}{n^{3} x - n^{2} x - n x - x}$ $g (x) = f^{″} (x)$ $\int_{ψ} \overset{δ}{} δ (x) d x \in R ∖ Q ?$ $t r u e o r f a l s e ?$
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