Question

Si
$f(x) = \frac{1}{x - 1}$
y
g(x) = raiz cuadrada de x
Encontrar dominio de :
(f+g)(x)=
(f-g)(x)=
(f*g)(x)=
(f/g)(x)=
(g/f)(x)=

Urgente :c​

Answer 1

Respuesta:

Propiedades de operaciones en funciones

$(f +g)(x)=f(x)+g(x)\\(f-g)(x)=f(x)-g(x)\\(f \ . \ g ) ( x ) = f (g(x))\\\\\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)} \ ;\ \ g\ne \:0$

------------------------------------------------------------------------

$(f+g)(x)=\frac{1}{x-1}+\sqrt{x}=\frac{1+\sqrt{x}\left(x-1\right)}{x-1}$

$(f-g)(x)=\frac{1}{x-1}-\sqrt{x}=\frac{1-\sqrt{x}\left(x-1\right)}{x-1}$

$(f \ . \ g)(x)=\frac{1}{\sqrt{x}- 1}$

$\left(\frac{f}{g}\right)\left(x\right)=\frac{\frac{1}{x-1}}{\sqrt{x} }=\frac{1}{\left(x-1\right)\sqrt{x}}=\frac{\sqrt{x}}{x\left(x-1\right)}$

$\left(\frac{g}{f}\right)\left(x\right)=\frac{\sqrt{x}}{\frac{1}{x-1}}=\frac{\sqrt{x}\left(x-1\right)}{1}=\sqrt{x}\left(x-1\right)$