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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