Given:
[tex]f(x)=\frac{1}{x}\colon g(x)=x^2+5x[/tex]
so (f.g)(x) is:
[tex]fg(x)=\frac{1}{x^2+5x}[/tex]
Domain: domain is define as a all possible input where function is define is know as a domain of function.
[tex]\text{Domain}=\text{ x}\in R\colon x\ne5\text{ and x}\ne0[/tex]
Range: range is define as a output of function
and the function output is:
so the range of function is
[tex]\text{Range y}\in R\colon y\leq\frac{-4}{25}\text{ or }y>0[/tex]
