Composition Chains Math Example 3

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Example 3

easy
Given f(x)=3x−1f(x)=3x-1 and g(x)=x2g(x)=x^2, find (f∘g)(x)(f\circ g)(x) and evaluate it at x=2x=2.

Solution

  1. 1
    (f∘g)(x)=f(g(x))=f(x2)=3(x2)−1=3x2−1(f\circ g)(x)=f(g(x))=f(x^2)=3(x^2)-1=3x^2-1.
  2. 2
    (f∘g)(2)=3(4)−1=12−1=11(f\circ g)(2)=3(4)-1=12-1=11.

Answer

(f∘g)(x)=3x2−1(f\circ g)(x)=3x^2-1; (f∘g)(2)=11(f\circ g)(2)=11
To compose f∘gf\circ g, replace every occurrence of xx in ff with the entire expression g(x)g(x). Here f(x)=3x−1f(x)=3x-1 becomes f(g(x))=3(x2)−1=3x2−1f(g(x))=3(x^2)-1=3x^2-1.

About Composition Chains

A composition chain is a sequence of functions applied one after another: (f∘g∘h)(x)=f(g(h(x)))(f \circ g \circ h)(x) = f(g(h(x))), evaluated inside-out from right to left.

Learn more about Composition Chains →

More Composition Chains Examples

Example 1 easy

Let [formula], [formula], [formula]. Compute [formula] step by step.

Example 2 medium

Find the formula for [formula] and [formula] where [formula] and [formula]. Show they are not equal.

Example 4 hard

Decompose [formula] as a composition [formula] of three simpler functions.

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