Respuesta :
Answer:
1) (f + g)(x) : Domain (-∞, ∞)
2) (f - g)(x) : Domain (-∞, ∞)
3) (fg)(x) : Domain (-∞, ∞)
4) (f×g)(x) : Domain (-∞, ∞)
Step-by-step explanation:
Since given functions are f(x) = x - 3 and g(x) = x²
Then (f + g)(x) = f(x) + g(x)
= (x - 3) + x²
Since for every of x the given function is defined
Therefor, domain of (f + g)(x) will be defined by (-∞, ∞).
Since, (f - g)(x) = f(x) - g(x)
Now we put the values of f(x) and g(x)
(f - g)(x) = (x - 3) - x²
Since for every value of x, (f - g)(x) is defined.
Therefor, domain of (f - g)(x) will be (-∞, ∞)
SInce, (fg)(x) = f [ g(x) ]
Now f{ g(x) ] = (x²) - 3
= x² - 3
Again this function is defined for every value of x.
Therefore, domain of f[ g(x) ] will be (-∞, ∞).
At the last we have to find (f×g)(x) = f(x)×g(x)
= (x - 3)(x²)
Since this function is defined for all values of x
Therefore, domain of (f×g)(x) will be (-∞, ∞)
Answer:
[tex](f+g)(x)=x-3+x^2[/tex] ; Domain = (-∞, ∞)
[tex](f-g)(x)=x-3-x^2[/tex] ; Domain = (-∞, ∞)
[tex](fg)(x)=x^3-3x^2[/tex] ; Domain = (-∞, ∞)
[tex](\frac{f}{g})(x)=\frac{x-3}{x^2}[/tex] ; Domain = (-∞,0)∪(0, ∞)
Step-by-step explanation:
The given functions are
[tex]f(x)=x-3[/tex]
[tex]g(x)=x^2[/tex]
1.
[tex](f+g)(x)=f(x)+g(x)[/tex]
Substitute the values of the given functions.
[tex](f+g)(x)=(x-3)+x^2[/tex]
[tex](f+g)(x)=x-3+x^2[/tex]
The function [tex](f+g)(x)=x-3+x^2[/tex] is a polynomial which is defined for all real values x.
Domain of (f+g)(x) = (-∞, ∞)
2.
[tex](f-g)(x)=f(x)-g(x)[/tex]
Substitute the values of the given functions.
[tex](f-g)(x)=(x-3)-x^2[/tex]
[tex](f-g)(x)=x-3-x^2[/tex]
The function [tex](f-g)(x)=x-3-x^2[/tex] is a polynomial which is defined for all real values x.
Domain of (f-g)(x) = (-∞, ∞)
3.
[tex](fg)(x)=f(x)g(x)[/tex]
Substitute the values of the given functions.
[tex](fg)(x)=(x-3)x^2[/tex]
[tex](fg)(x)=x^3-3x^2[/tex]
The function [tex](fg)(x)=x^3-3x^2[/tex] is a polynomial which is defined for all real values x.
Domain of (fg)(x) = (-∞, ∞)
4.
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)}[/tex]
Substitute the values of the given functions.
[tex](\frac{f}{g})(x)=\frac{x-3}{x^2}[/tex]
The function [tex](\frac{f}{g})(x)=\frac{x-3}{x^2}[/tex] is a rational function which is defined for all real values x except 0.
Domain of (f/g)(x) = (-∞,0)∪(0, ∞)
