Respuesta :
Answer:
The sum of all real numbers x that are not in the domain of the function f(x) is 2.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{x^2-7}+\frac{1}{x^3-8}+\frac{1}{x^4-9}[/tex]
The domain is the set of inputs. So, the domain of the given function is all real numbers except those numbers for which denominator values is equal to 0.
[tex]x^2-7=0[/tex]
[tex]x^2=7[/tex]
[tex]x=\pm \sqrt{7}[/tex]
It means [tex]\pm \sqrt{7}[/tex] is not included in domain.
[tex]x^3-8=0[/tex]
[tex]x^3=8[/tex]
[tex]x=2[/tex]
It means 2 is not included in domain.
[tex]x^4-9=0[/tex]
[tex]x^4=9[/tex]
[tex]x^2=\pm 3[/tex]
[tex]x=\pm \sqrt{3}[/tex]
It means [tex]\pm \sqrt{3}[/tex] is not included in domain.
The sum of all real numbers x that are not in the domain of the function f(x) is
[tex]Sum=-\sqrt{7}+\sqrt{7}+\sqrt{3}-\sqrt{3}+2=2[/tex]
Therefore the sum of all real numbers x that are not in the domain of the function f(x) is 2.
