Function Composition Math Example 1

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

Example 1

easy
Given f(x)=2x+1f(x) = 2x + 1 and g(x)=x2g(x) = x^2, find (f∘g)(3)(f \circ g)(3).

Solution

  1. 1
    (f∘g)(3)(f \circ g)(3) means f(g(3))f(g(3)), so evaluate the inner function first.
  2. 2
    Compute g(3)=32=9g(3) = 3^2 = 9.
  3. 3
    Substitute that result into ff: f(9)=2(9)+1=19f(9) = 2(9) + 1 = 19.

Answer

1919
Function composition works from the inside out: evaluate the inner function first, then feed its output into the outer function.

About Function Composition

Function composition applies one function to the output of another: (f∘g)(x)=f(g(x))(f \circ g)(x) = f(g(x)), meaning evaluate gg first, then apply ff to the result.

Learn more about Function Composition →

More Function Composition Examples

Example 2 medium

Given [formula] and [formula], find the formula for [formula].

Example 3 easy

Given [formula] and [formula], find [formula].

Example 4 hard

Given [formula] and [formula], find the domain of [formula].

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FunctionInverse Function