Let f and g be a function. Composite function formula can be denoted by:
(f o g)(x) = f(g(x))
Example 1.
f(x) = x + 3
g(x) = x - 7
(f o g)(x) = f(g(x))
f(g(x)) = x + 3
f(g(x)) = g(x) + 3
f(g(x)) = x - 7 + 3
f(g(x)) = x - 4
Example 2.
f(x) = x + 7/x-3
g(x) = x - 2
(f o g)(x) = f(g(x))
f(g(x)) = x + 7/x - 3
f(g(x)) = g(x) + 7/ g(x) - 3
f(g(x)) = x - 2 + 7/x - 2 - 3
f(g(x)) = x + 5/ x - 5
Example 3.
f(x) = x^2 - 3x + 9
g(x) = x - 2
(f o g)(x) = f(g(x))
f(g(x)) = x^2 - 3x + 9
f(g(x)) = (x - 2)^2 - 3(x - 2) + 9
f(g(x)) = x^2 - 4x + 4 - 3x + 6 + 9
f(g(x)) = x^2 - 7x + 19
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