Respuesta :
Answer:
1) [tex] {\bf f }\circ {\bf g}(x) ={\bf x^2}-{\bf6x}+{\bf9}[/tex] and [tex] {\bf g }\circ {\bf f}(x)={\bf x^2}-{\bf3}[/tex] are not equal
ie,[tex] {\bf f} \circ {\bf g}(x) \neq {\bf g} \circ{\bf f}(x)[/tex]
2) The domain is x
Step-by-step explanation:
Given functions are [tex]f(x)=x^2[/tex] and [tex] g(x) = x-3 [/tex]
now find the composition of two functions verify that
[tex] f \circ g = g {\circ} f [/tex]
now find the composition of [tex] f\circ g[/tex]
[tex] f \circ g=f(g(x))[/tex]
[tex] f \circ g=f(x-3)[/tex]
[tex] f \circ g=(x-3)^2[/tex]
[tex] f \circ g=x^2-2(x)(3)+3^2[/tex]
[tex] f \circ g=x^2-6x+9[/tex]
now find the composition of [tex] g \circ f[/tex]
[tex] g \circ f=g(f(x))[/tex]
[tex] g \circ f=g(x^2)[/tex]
[tex] g \circ f=x^2-3[/tex]
Comparing the above two compositions we get
[tex] f \circ g = x^2-6x+9[/tex] and [tex] g \circ f= x^2-3[/tex] are not equal
ie, [tex] f \circ g \neq g \circ f[/tex].
2) Given that the composition of two function is x-3
Let the functons be f(x) and g(x)
so the composition of two function [tex] f \circ g=x-3[/tex]
it may be written as [tex] f(g(x))=x-3 [/tex]
[tex] g(x)=f^{-1}(x-3)[/tex]
[tex] g(x)=x-3[/tex]
