Respuesta :

Find the third iterate, x3, of the function f(x) = 3x + 5 for an initial value of x0 = 1. x1 = 3(1) + 5 = 8 ... x2 = 3(8) + 5 = 29 ... x3 = 3(29) + 5 = 92 

The value of a third iterate, x₃ is 92.

What is an Iterated Function?

  • This function is obtained by composing a different function with itself for number of times.
  • In this we start with some initial object value and the result of this applied value is again used as an input for the function and it is repeated again.

Given: Function

f(x) = 3x + 5

initial value (x₀) = 1

We have to find the third iterate, x₃.

The value of first iterate is given by:

⇒ x₁ = f(x₀) = 3x₀ + 5

∵ x₀ = 1

⇒ x₁ = f(1) = 3(1) + 5

⇒ x₁ = 8

The value of second iterate  is given by:

⇒ x₂ = f(x₁) = 3x₁ + 5

∵ x₁ = 8

⇒ x₂ = f(8) = 3(8) + 5

⇒ x₂ = 29

The value of third iterate is given by:

⇒ x₃ = f(x₂) = 3x₂ + 5

∵ x₂ = 29

⇒ x₃ = f(29) = 3(29) + 5

⇒ x₃ = 92

Therefore, for a given function the value of the third iterate, x₃ is 92.

Learn more about the Iterated Function here: https://brainly.com/question/2141583?referrer=searchResults

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