Question

Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?

Answer 1

First part

To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.

$\begin{gathered} f(-2)=\frac{1}{3}(-2)^3 \\ f(-2)=\frac{1}{3}(-8) \\ f(-2)=-\frac{8}{3} \end{gathered}$

Second part

To find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.

$\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}$

Finally, we find the value of the given expression:

$\begin{gathered} 6f(-2)+3g(1)=6\cdot-\frac{8}{3}+3\cdot3 \\ 6f(-2)+3g(1)=-\frac{6\cdot8}{3}+9 \\ 6f(-2)+3g(1)=-\frac{48}{3}+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}$