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# Calculus Early Transcendentals

Authors:
James Stewart
Exercise:
True-false Quiz
Chapter:
Functions And Models
Edition:
7
ISBN:
9780538497909
Question:
1
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### Question

If $f$ is a function, then $f(s+t)=f(s)+f(t)$ (true/false).

The statement is False.

$f(s+t)\neq f(s)+f(t)$

Consider $f(x)=x+1, s=1, and \ t=-1$

$\\ \begin{equation} \\ f(s+t) = f(1-1)\\ \ \ \ \ \ \ = f(0)\\ \ \ \ \ \ \ \ = 0+1\\ \ \ = 1 \end{equation} \\ \begin{equation}\\f(s)+f(t)= f(1)+f(-1)\\ \ \ \ \ \ \ \ \ \ = (1+1)+(-1+1)\\ =2+0\\=2 \end{equation}$

$\therefore f(s+t)\neq f(s)+f(t))$

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