MHB Finding f/g: Composite Functions

[needhelpplease]

The questions is asking me to find \frac{f}{g} basically , the question is asking me to find the answer , even though i know it, i can't get my head around it.

the composite function is

f(x)=x^2+1
g(x)=1/x

we need to find foG (f of g) [composite functions].

 

[needhelpplease]

The questions is asking me to find \frac{f}{g} basically , the question is asking me to find the answer , even though i know it, i can't get my head around it.

the composite function is

f(x)=x^2+1
g(x)=1/x

we need to find foG (f of g) [composite functions].

Thank you solved.Divide them both so x^2+1 / 1/x
switch them to multiply so it's going to be x^2+1/x

 

[evinda]

$f \circ g(x)= f(g(x))=\frac{1}{x^2}+1$

 

[I like Serena]

Additionally, the quotient (which is not the composite $f \circ g$) is:
$$\frac fg(x) = \frac{f(x)}{g(x)}=\frac{x^2+1}{1/x}=(x^2+1)x=x^3+x$$

 

[MarkFL]

Just to add an intermediary step:

$$(f\circ g)(x)=f(g(x))=f\left(\frac{1}{x}\right)=\left(\frac{1}{x}\right)^2+1=\frac{1}{x^2}+1$$