Answer:
[tex]g(x)=x^2+4[/tex] and [tex]f(x)=\frac{8}{x}[/tex]
Step-by-step explanation:
If we want to express [tex]y[/tex] as [tex]y=f(g(x))[/tex], this means that put the function [tex]g(x)[/tex] into [tex]x[/tex] of [tex]f(x)[/tex] to get [tex]y[/tex].
The function [tex]y[/tex] is given as [tex]y=\frac{8}{x^{2}+4}[/tex]
So we need to figure out a function [tex]g(x)[/tex] that we can put into another [tex]f(x)[/tex] to get [tex]y[/tex]
If we let [tex]g(x)=x^2+4[/tex] and [tex]f(x)=\frac{8}{x}[/tex], we can clearly see that putting g(x) into x of f(x) will give us [tex]\frac{8}{x^2+4}[/tex], which is y.
Hence [tex]g(x)=x^2+4[/tex] and [tex]f(x)=\frac{8}{x}[/tex]
Answer:
[tex]f(x)=x+4[/tex]
[tex]g(x)=\frac{8}{x^2}[/tex]
Step-by-step explanation:
we are given
we are given
[tex]y=\frac{8}{x^2}+4[/tex]
Since, we have to identify f(x) and g(x)
where g(x) is inner function
Let's assume
[tex]g(x)=\frac{8}{x^2}[/tex]
so, we get
[tex]y=g(x)+4[/tex]
we know that
y=f(g(x))
so, we can also write as
[tex]f(g(x))=g(x)+4[/tex]
now, we can replace g(x) as x
we get
[tex]f(x)=x+4[/tex]
so, we get
[tex]f(x)=x+4[/tex]
[tex]g(x)=\frac{8}{x^2}[/tex]
