1. 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].

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 gonna be x^2+1/x

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

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

5. Just to add an intermediary step:

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