If ∀x ∈ {1,2,3,4} , $f$(x) = $ x^2 $ and ∀x ∈ {2,4,3,6} , $g$(x) = $ x+1 $.
Find $ (g\; o\; f ), (f\; o\; g)\; and \;Im(f \;o \;g)$
I dont understand the question much. If someone can help me it would be really helpful.
$ (g\; o\; f ) (x)$ = $g(f(x)) = x^2 + 1$
$ (f\; o\; g ) $ = $f(g(x)) = (x+1)^2$
Is this what they are expecting as an answer or is there more for it?
The formulas are correct. However, maybe the question is also asking to find the domains and ranges. For example, note that $(f \;o \;g)(6)$ is simply undefined because $g(6)=7$ is not in the domain of $f$.