Composition of Functions
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Definition of Composition of Functions
Composition of Functions is the process of combining two functions where one function is performed first and the result of which is substituted in place of each x in the other function.
More About Composition of Functions
 The composition of functions f and g is written as f o g.
 [f o g](x) = f[g(x)]
 Composition of functions is not commutative. f[g(x)] is generally not equal to g[f(x)].
For example, consider f(x) = 2x and g(x) = x  3.
f[g(x)] = 2(x  3) = 2x  6
g[f(x)] = (2x)  3 = 2x  3
f[g(x)] is not equal to g[f(x)].
Video Examples: Function Compositions
Solved Example onComposition of Functions
Ques: Evaluate the composite function f[g(x)] for f(x) = 3x2 + 6 and g(x) = x  8.
Choices:

A. x  8
B. 3x2  48x + 198
C. 3x2  2
D. 3x2 + 6
Correct Answer: B
Solution:

Step 1: f[g(x)] = f[x  8]
Step 2: = 3(x  8)2 + 6
Step 3: = 3(x2  16x + 64) + 6
Step 4: = 3x2  48x + 198.
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