Answer
The statement “$f\left( x+h \right)=f\left( x \right)+f\left( h \right)$" is false.
Work Step by Step
Let us consider the function $f\left( x+h \right)=f\left( x \right)+f\left( h \right)$.
$f\left( x+h \right)$ is one function whereas $f\left( x \right)$ and $f\left( h \right)$ are other functions.
Let us assume an example shown below:
The function is $f\left( x \right)=x+1$ , and we have $f\left( x+1 \right)$
Replace $x$ by $\left( x+1 \right)$ in the above-mentioned expression to get
$\begin{align}
& f\left( x \right)=x+1 \\
& f\left( x+1 \right)=\left( x+1 \right)+1 \\
& f\left( x+1 \right)=x+2
\end{align}$
Now, Substitute x by 1 in the function $f\left( x \right)=x+1$ and get
$\begin{align}
& f\left( x \right)=x+1 \\
& f\left( 1 \right)=1+1 \\
& =2
\end{align}$
Thus:
$\begin{align}
& f\left( x+1 \right)\ne f\left( x \right)+f\left( 1 \right) \\
& f\left( x+1 \right)\ne x+1+2 \\
& f\left( x+1 \right)\ne x+3 \\
\end{align}$
Therefore, the expression $f\left( x+h \right)=f\left( x \right)+f\left( h \right)$ is false and invalid.
