Composition Chains Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Let f(x)=x+1f(x)=x+1, g(x)=2xg(x)=2x, h(x)=x2h(x)=x^2. Compute (f∘g∘h)(3)(f\circ g\circ h)(3) step by step.

Solution

  1. 1
    Start from the innermost function: h(3)=32=9h(3)=3^2=9.
  2. 2
    Apply gg: g(h(3))=g(9)=2(9)=18g(h(3))=g(9)=2(9)=18.
  3. 3
    Apply ff: f(g(h(3)))=f(18)=18+1=19f(g(h(3)))=f(18)=18+1=19. So (f∘g∘h)(3)=19(f\circ g\circ h)(3)=19.

Answer

(f∘g∘h)(3)=19(f\circ g\circ h)(3) = 19
Function composition chains are evaluated from right to left (innermost to outermost). The output of each function becomes the input of the next. Keeping track of this order is essential for correct computation.

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 2 medium

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

Example 3 easy

Given [formula] and [formula], find [formula] and evaluate it at [formula].

Example 4 hard

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

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