Answer:
Domain is all real number except [tex]-2[/tex]
Step-by-step explanation:
[tex]f(x)= x+2[/tex] and [tex]g(x)= \frac{1}{x+2}[/tex]
now we find fg
[tex]fg= f(x) * g(x)[/tex]
Replace f(x) and g(x)
[tex]f(x) * g(x)= (x+2)*\frac{1}{x+2}[/tex]
[tex]f(x) * g(x)=\frac{x+2}{x+2}[/tex]
We have x+2 at the top and bottom. cancel it out
So we have hole at x+2
set the denominator =0 and solve for x
[tex]x+2=0[/tex]
Subtract 2 on both sides
[tex]x=-2[/tex]
the value of x cannot be [tex]-2[/tex]
Domain is all real number except [tex]-2[/tex]
