if-the-combined-function-is-h-x-3x-2-1-then-find-the-tow-other-functions-of-its-

Question Number 192048 by sciencestudentW last updated on 06/May/23

i f t h e c o m b i n e d f u n c t i o n i s h (x) = \sqrt{3 x^{2} + 1}

t h e n f i n d t h e t o w o t h e r f u n c t i o n s o f i t s .

Commented by AST last updated on 07/May/23

I f “ {c o m b i n e d}^{″} h e r e m e a n s h (x) = f (g (x)),

f (x) = \sqrt{x}, g (x) = 3 x^{2} + 1 i s a p o s s i b i l i t y .

Answered by mehdee42 last updated on 07/May/23

s u p p o s e; f (x) = \sqrt{a x + b}; a \neq 0, g (x) = a^{'} x^{2} + b^{'} x + c^{'}; a^{'} \neq 0

f o g (x) = f (g (x)) \Rightarrow \sqrt{a (a^{'} x^{2} + b^{'} x + c^{'}) + b} \equiv \sqrt{3 x^{2} + 1}

\Rightarrow {a a}^{^{'}} = 3 & {a b}^{'} = 0 & {a c}^{'} + b = 1

f o r d i f f r e n t v a l u e s a, b, a^{'}, b^{'}, c^{'} v a r i u o s f u n c t i o n s

c a n b e o b t a i n e d . f o r e x a m p l e :

a = 1, b = 1, a^{'} = 3, b^{'} = 0 & c^{'} = 0

\Rightarrow f (x) = \sqrt{x + 1} & g (x) = 3 x^{2}

o r; a = 3, b = - 2, a^{'} = 1, b^{'} = 0 & c^{'} = 1

\Rightarrow f (x) = \sqrt{3 x - 2} & g (x) = x^{2} + 1

a n d s o o n

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