Question

ayuda
tengo que encontrar esto:
f(X)= √x+1 g(x)=1/x^2-1

a. (fof)(x)
b.(gog)
c. (fog)(3)
d.(gof)(4)

Answer 1

Son composición de funciones. Sea $f(x)= \sqrt{x+1}$ y $g(x)= \frac{1}{ x^{2} -1}$:

a) (fof)(x) = f(f(x)) = $\sqrt{ \sqrt{x+1} +1}$

b) (gog)(x)= g(g(x)) = $\frac{1}{ \frac{1}{ x^{2} -1}-1 } = \frac{ x^{2} -1}{- x^{2} } = \frac{1}{ x^{2} } -1$

c) (fog)(x) = f(g(x)) = $\sqrt{ \frac{1}{ x^{2} }+1 }$

Evaluando:

$f(g(3))= \sqrt{ \frac{1}{ 3^{2} -1}+1 } = \frac{3}{2 \sqrt{2} }$

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

Evaluando:

$g(f(4))= \frac{1}{4}$

Un saludo.