Composition of Functions Worksheets

Composition of functions f(g(x)) is nothing but combining two functions where the output of one function g(x) becomes the input of the other f(x). Keep a watch on the order as a change in the order may result in a different answer; f(g(x)) may not be the same as g(f(x)). For instance, to compose (fog)x, when f(x)= 6x2-2x+1 and g(x)= 3x, just rewrite the composition in the form f(g(x)), replace every occurrence of x in the outer function f(x) with g(x) the inner function, as in 6(3x)2-2(3x)+1. Simplify the expression and you are left with 54x2-6x+1. Augment skills in combining functions like the ones above with these composition of two functions worksheets.

These pdf worksheets are most appropriate for high school students.

CCSS: HSF-BF.A.1

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Composition of Two Functions
Worksheet 1
Worksheet 2