Question

Find the period of x + 3

Answer 1

ANSWER on Question #80062 – Math – Algebra

QUESTION

Find the period of the function

$$f(x) = x + 3$$

SOLUTION

By the definition, the period of the function is

$$\exists P \neq 0: f(x + P) = f(x)$$

(More information: https://en.wikipedia.org/wiki/Periodic_function)

In our case,

$$f(x) = x + 3 \rightarrow f(x + P) = (x + P) + 3 \rightarrow$$ $$\left\{ \begin{array}{c} f(x) = x + 3 \\ f(x + P) = x + P + 3 \rightarrow x + 3 = x + P + 3 \rightarrow P = x + 3 - x - 3 \rightarrow \boxed{P = 0} \\ f(x) = f(x + P) \end{array} \right.$$

Conclusion,

$$\boxed{f(x) = x + 3 \text{ is non-periodic function}}$$

ANSWER

$$f(x) = x + 3 \text{ is non-periodic function}$$

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