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f-x-1-a-x-1-a-x-and-D-f-g-x-ax-1-f-1-ax-a-find-D-g-




Question Number 155231 by mnjuly1970 last updated on 27/Sep/21
     f (x) :=(√((1/a) +x)) −(√((1/a) −x))    and    D_f  ≠ ∅ ,         g(x)=(√((ax−1)/(f^( −1) ( ax −a ))))          find :  D_( g)  =?
$$ \\ $$$$\:\:\:{f}\:\left({x}\right)\::=\sqrt{\frac{\mathrm{1}}{{a}}\:+{x}}\:−\sqrt{\frac{\mathrm{1}}{{a}}\:−{x}} \\ $$$$\:\:{and}\:\:\:\:\mathrm{D}_{{f}} \:\neq\:\varnothing\:, \\ $$$$\:\:\:\:\:\:\:{g}\left({x}\right)=\sqrt{\frac{{ax}−\mathrm{1}}{{f}^{\:−\mathrm{1}} \left(\:{ax}\:−{a}\:\right)}} \\ $$$$\:\:\:\:\:\:\:\:{find}\::\:\:\mathrm{D}_{\:{g}} \:=? \\ $$

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