Composite function:

If ƒ: x → y and g: y → z then we describe the composite function (goƒ): x → z by (goƒ) (x) ≡ g {f(x)}. To get (goƒ)(x), we first get the f-image of an element x∈x so that f(x)∈y, which is the domain of g(x). Then obtain g-image of f(x), i.e.g (f(x)) which could be an element of z.

• (g( ƒ (x₁))= g(y₂)=z₃.

• Range (goƒ) = {z₂,z₃} But Range (g) = {z₁,z₂,z₃}

• Obviously domain (gof) = {x : x ∈ Domain( ƒ ), ƒ (x) ∈ domain(g)}

• Same as we may define, (fog)x = f(g(x)) and domain (fog) = {x : x ∈ Domain(g), g(x) ∈ domain(f)}. In general fog ≠ gof.

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