Respuesta :
Answer:
[tex]h(f o g(x)) = f(g(x))= f(3x-5) = (3x-5)^9[/tex]
And we see that we satisfy the condition that
h (x)= (3x - 5)^9
So then our solution for this case is correct:
[tex] f(x) = x^9[/tex]
[tex] g(x) = 3x-5[/tex]
Step-by-step explanation:
For this case we can define the following functions:
[tex] f(x) = x^9[/tex]
[tex] g(x) = 3x-5[/tex]
And we can define [tex]h(x) = (f o g) (x)[/tex]
And if we solve for the last expression we got:
[tex]h(f o g(x)) = f(g(x))= f(3x-5)[/tex]
And using the function f(x) we got:
[tex]h(f o g(x)) = f(g(x))= f(3x-5) = (3x-5)^9[/tex]
And we see that we satisfy the condition that
h (x)= (3x - 5)^9
So then our solution for this case is correct:
[tex] f(x) = x^9[/tex]
[tex] g(x) = 3x-5[/tex]
The [tex](fog)x[/tex] is a composite function. [tex]f o g[/tex] means g(x) function is in f(x) function.
The composition of two function is, [tex]h(x)=(f o g)(x)=(3x-5)^{9}[/tex]
Where [tex]f(x)=x^{9}[/tex] and [tex]g(x)=3x-5[/tex]
A function , which is composition of two function known as composite function.
Here given that, [tex]h(x)=(f o g)(x)=(3x-5)^{9}[/tex]
Since, [tex]f o g[/tex] means g(x) function is in f(x) function.
[tex]f(x)=x^{9}[/tex] and [tex]g(x)=3x-5[/tex]
[tex]h(x)=f(g(x))=f(3x-5)=(3x-5)^{9}[/tex]
Therefore, our assumption is correct.
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