Question

Dadas las funciones: f(x) = √ 2 + 2 2 ; g(x) = 2 x−1 Hallar: i). (fog)(x) = ? ii). (f-1 o g) (x) = ?​

Answer 1

Datos:

$f(x)=\sqrt{2}+2x\\\\g(x)=2x-1$

Explicación paso a paso:

i)

$(f\circ g)(x)=f(g(x))\\\\(f\circ g)(x)=f(2x-1)\\\\(f\circ g)(x)=\sqrt{2}+2(2x-1) \\\\(f\circ g)(x)=\sqrt{2}+4x-2$

ii)

$\sqrt{2}+2x=y \\\\2x=y-\sqrt{2}\\\\x=\frac{y-\sqrt{2} }{2}$

$f^{-1}(x)=\frac{x-\sqrt{2} }{2}$

$(f^{-1} \circ g)(x)=f^{-1}(2x-1)\\\\(f^{-1} \circ g)(x)=\frac{2x-1-\sqrt{2} }{2}$