Composition of functions of given set

Question

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?

For both compositions, I think you have to check that the result of the inner function is in the domain of the outer function, e. g. $f(g(6))$ is not defined — Zubin Mukerjee, Sep 25 '18 at 15:31

score 1 · Accepted Answer · answered Sep 25 '18 at 15:25

1

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 $f$.

answered Sep 25 '18 at 15:25

Mark

39,605

So if we consider $(fog)(3) then f(g(3)) = f(4)$ we say its defined? – Shehan Tearz Sep 26 '18 at 03:55
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$(f\circ g)(3)$ is defined, yes. – Mark Sep 26 '18 at 08:03

Composition of functions of given set

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