a) (f-t)(x) ... se realizan las operaciones con los términos semejantes D(f-t)(x)=xER
= x^2-x-2 - 1-x^2
= -x-3
b) (f/h)(x) ... aquí se usa la ley de extremos y medios D(f/h)(x)= xER-{-2,2}
= [tex] \frac{ x^2-x-2}{ \frac{1}{x^2-4}} } [/tex]
=[tex] \frac{x^2-x-2}{x^2-4}
[/tex]
c) (hog)(x) ... se cancela raiz con pontencia--- D(hog)(x)=xER-{4}
= [tex]
\frac{1}{ \sqrt{2x-4})^2 -4} [/tex]
= [tex] \frac{1}{2x-4-4 } = \frac{1}{2x-8} [/tex]
d) (got)(x) D(got)(x)=xER+ {0}
= [tex] \sqrt{2(1-x^2) -4[/tex]
=[tex] \sqrt{2(x+1)(x-1) -4} [/tex]
=[tex] \sqrt{2x+2+2x-2-4} [/tex]
=[tex] \sqrt{4x-4} [/tex]
e) (f·h)(x) D(f·h)(x)=xER-{-2,2}
= x^2-x-2 * [tex] \frac{1}{x^2-4} [/tex]
=[tex] \frac{x^2-x-2}{x^2-4} [/tex]
f) f^-1(x) D(f^-1)=xER-{1}
x= y^2-y-2
x=(y-1)(y-1)
x(y-1)=y-1
xy-x=y-1
xy-y=x-1
y(x-1)=x-1
y=[tex] \frac{x-1}{x-1}[/tex]
g) (f/t)(x) D(f/t)= xER-{1}
=[tex] \frac{x^2-x-2}{1-x^2} [/tex]
h) g^-1(x) D(g^-1)=xER
x= [tex] \sqrt{2y-4} [/tex]
x^2=2y-4
x^2+4=2y
[tex] \frac{x^2+4}{2} [/tex] =y
i) h^-1(x) d(h^-1) = xER+ - {0}
x=[tex] \frac{1}{y^2-4} [/tex]
x(y^2-4)=1
xy^2-4x=1
xy^2=1-4x
y^2= [tex] \frac{1+4x}{x} [/tex]
y=[tex] \sqrt{ \frac{4x+1}{x} } [/tex]
j) t^-1(x) D(t^-1)=xER+
x=1-y^2
x+y^2=1
y^2=1-x
y=[tex] \sqrt{1-x} [/tex]
