Question

For f(x) = x - 3 and g(x) = x^2 + 1, what are the follow?
a) What are (f o g)(3)? (g o f)(3)? (f o f)(3)?
b) What is the domain and range of f? of g?

explain & show your work please. I don't understand this. ):

Answer 1

both of these are polynomials, so the implied domain for both is all real numbers. you can evaluate a polynomial at any number

Answer 2

the range of f is all real numbers because it is a line
the range of g is
\[[1,\infty)\] because
\[x^2\geq0\] and so
\[x^2+1\geq1\]

Answer 3

\[f\circ g(x)=f(g(3))=f(3^2+1)=f(10)=10-3=7\]

Answer 4

\[g\circ f(3)=g(f(3))=g(3-3)=g(0)=0^2+1=1\]

Answer 5

\[f\circ f(x)=f(f(3))=f(3-3)=f(0)=0-3=-3\]