If-f-x-x-ax-2-bx-3-obtain-f-x-3-up-to-x-3-

Question Number 7752 by Tawakalitu. last updated on 14/Sep/16

I f f (x) = x + {a x}^{2} + {b x}^{3} + \dots . o b t a i n \sqrt{f (x^{3})}

u p t o x^{3}

Commented by FilupSmith last updated on 14/Sep/16

f (x) = x^{1} a_{0} + x^{2} a_{1} + x^{3} a_{2} + \dots

∴ f (x^{t}) = \underset{n = 0}{\sum^{k}} x^{t + n} a_{n} = x^{t - 1} \underset{n = 0}{\sum^{k}} x^{n + 1} a_{n}

∴ f (x^{3}) = x^{3} (a_{0} + {x a}_{1} + \dots) = x^{2} f (x)

f (x^{3}) = x^{2} f (x)

∴ \sqrt{f (x^{3})} = x \sqrt{f (x)}

Commented by Tawakalitu. last updated on 14/Sep/16

I r e a l l y a p p r e c i a t e s i r . t h a n k y o u .

Commented by Rasheed Soomro last updated on 14/Sep/16

f (x) = x^{1} a_{0} + x^{2} a_{1} + x^{3} a_{2} + \dots

f (x^{t}) = {(x^{t})}^{1} a_{0} + {(x^{t})}^{2} a_{1} + {(x^{t})}^{3} a_{2} + \dots .

f (x^{t}) = x^{t \times 1} a_{0} + x^{t \times 2} a_{1} + x^{t \times 3} a_{2} + \dots .

f (x^{t}) = \underset{n = 0}{\sum^{k}} x^{t \times (n + 1)} a_{n} o r f (x^{t}) = \underset{n = 1}{\sum^{k}} x^{t \times n} a_{n - 1}

I m a y b e w r o n g . I^{'} m n o t s u r e .

Commented by ajaenuri86@gmail.com last updated on 14/Sep/16

t r u e

Commented by Tawakalitu. last updated on 14/Sep/16

T h a n k s f o r y o u r c o n t r i b u t i o n s i r .

Commented by Rasheed Soomro last updated on 15/Sep/16

f (x) = x^{1} a_{0} + x^{2} a_{1} + x^{3} a_{2} + \dots

f (x^{t}) = \underset{n = 0}{\sum^{k}} x^{t + n} a_{n} ? ? ?

- - - - - - - - -

f (x) = x^{1} a_{0} + x^{2} a_{1} + x^{3} a_{2} + \dots

f (x^{t}) = {(x^{t})}^{1} a_{0} + {(x^{t})}^{2} a_{1} + {(x^{t})}^{3} a_{2} + \dots

= x^{t \times 1} a_{0} + x^{t \times 2} a_{1} + x^{t \times 3} a_{2} + \dots \dots

\overset{?}{=} \underset{n = 0}{\sum^{k}} x^{t + n} a_{n} ? ? ?