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f-x-a-x-1-x-D-f-0-a-1-h-x-f-1-a-ax-f-1-a-2x-D-h-D-Domain-




Question Number 151958 by mnjuly1970 last updated on 24/Aug/21
f ( x ) = a −(√((x/(1+x)) ))   , D_( f)  : [ 0, ∞)  , a≥ 1   ,  h (x ):=(√(( f^( −1) (a−ax ))/(f^( −1) ( a− 2x ))))            D_( h)  = ?   (   D := Domain )
$${f}\:\left(\:{x}\:\right)\:=\:{a}\:−\sqrt{\frac{{x}}{\mathrm{1}+{x}}\:}\:\:\:,\:{D}_{\:{f}} \::\:\left[\:\mathrm{0},\:\infty\right) \\ $$$$,\:{a}\geqslant\:\mathrm{1}\:\:\:,\:\:{h}\:\left({x}\:\right):=\sqrt{\frac{\:{f}^{\:−\mathrm{1}} \left({a}−{ax}\:\right)}{{f}^{\:−\mathrm{1}} \left(\:{a}−\:\mathrm{2}{x}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:\:\:{D}_{\:{h}} \:=\:?\:\:\:\left(\:\:\:{D}\::=\:{Domain}\:\right) \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$

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