Question

Consideram funcția f:R->R, f(x) =3-2x. Calculati media geometrică a numerelor a=f(√2) si b=f(-√2)​

Answer 1

$f:\mathbb{R}\rightarrow\mathbb{R} \: \: \: ,f(x)=3-2x$

$a = f( \sqrt{2} ) = 3 - 2 \sqrt{2}$

$b = f( - \sqrt{2} ) = 3 - 2 \times ( - \sqrt{2} ) = 3 + 2 \sqrt{2}$

$m_{g} = \sqrt{ab}$

$m_{g} = \sqrt{(3 - 2 \sqrt{2} )(3 + 2 \sqrt{2} )}$

$m_{g} = \sqrt{ {3}^{2} - {(2 \sqrt{2} )}^{2} }$

$m_{g} = \sqrt{9 - 8}$

$m_{g} = \sqrt{1}$

$m_{g} = 1$