Input-Output View Math Example 4

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

Example 4

medium
Two function machines are connected: machine AA doubles the input, machine BB subtracts 11. Find the combined output for input x=5x=5, and write the combined formula.

Solution

  1. 1
    Machine AA: output =2x= 2x. Machine BB receives that output and subtracts 11: 2x−12x - 1.
  2. 2
    Combined formula: f(x)=2x−1f(x) = 2x - 1. For x=5x=5: f(5)=2(5)−1=9f(5) = 2(5)-1 = 9.

Answer

f(x)=2x−1f(x) = 2x-1; f(5)=9f(5) = 9
Chaining function machines corresponds to function composition. The output of the first machine becomes the input of the second. This builds intuition for composite functions before introducing the formal notation f∘gf \circ g.

About Input-Output View

The input-output view of a function treats it as a black box: put in a value (input), get out a uniquely determined value (output), without worrying about the internal mechanism.

Learn more about Input-Output View →

More Input-Output View Examples

Example 1 easy

Think of [formula] as a machine. Describe the sequence of operations applied to input [formula], the

Example 2 medium

A function machine applies two operations in sequence: first square the input, then add [formula]. W

Example 3 easy

A vending machine charges [formula]1.50[formula]C(n)[formula]n[formula]C(4)[formula][formula].

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