Chapter 5.8, Problem 20ES

True-False Determine whether the statement is true or false. Explain your answer. (Assume that $f$ and $g$ denote continuous functions on an interval $\left[a,b\right]$ and that $f_{\text{ave}}$ and $g_{\text{ave}}$ denote the respective average values of $f$ and $g$ on $\left[a,b\right]$ .)

The average value of a constant multiple of $f$ is the same multiple of $f_{\text{ave}}$ ; that is, if $c$ is any constant,

${\left(c\cdot f\right)}_{\text{ave}}=c\cdot f_{\text{ave}}$